Best-case scenario for the USSR in the Cold War is a shorter, less bloody WWII that doesn't devastate most of the most prosperous regions of the USSR and kill as many Soviets. That puts the USSR in the best position it would be possible for it to be in.
I agree. The earlier the POD the better (though that "US intervention in China and Hungary" by Admiral Matt is brilliant AND post-1945 - I wrote up most of this response yesterday night, before he posted), since it allows butterflies to erode some long-term disadvantages of the USSR (and advantages of the US). People in the West and in Russia always rail about the weaknesses of the Soviet system, and I'm not going to entirely disagree with them, the system had major weaknesses. Yet (post-WW2) Soviet and Russian problems also stem from externalities and circumstances that have to be dealt with. The Soviet Union put ideology first and foremost, but even they knew of the fact that the USSR was not only an ideological construct.
Let us review these externalities: The area of the Russian Empire made up the core of the USSR. Modernisation in the Empire only started arriving post-1860, particularly in the industrial and agricultural sectors of the economy. Still, it exported grain and Stolypin's reforms looked promising. French investment and railroads came to the country. Then all of this was cut short by WW1. From 1914 to 1921, the Russian Empire was in a state of war, whether fighting in a world war or the even bloodier and destabilising civil war from 1917-1921. The USSR formed from its ashes thus had a citizenry scarred by this. Then we had Stalin's less wise economic policies, particularly in agriculture. Then we had WW2, an absolute catastrophe. Frankly, the fact that this bombed out land which had suffered catastrophe after catastrophe from 1914 to 1945 enjoyed a period of prosperity/stability and challenged the untouched USA for global leadership is a miracle.
Next we must review its sphere of influence. Eastern Europe was developed in some ways, yes. Yet Eastern Europe was several countries cut out from the corspse of the Russian (see above) and Austro-Hungarian Empires. Things were a mess there as a result, and WW2 ruined them like it ruined the USSR. Compare to this to what the USA received in its sphere of influence: Western Europe, weakened enough so as to be unable to mount a challenge to the US, but strong enough to provide fuel to the American economy, and Japan. The USSR also received various undeveloped allies, mostly money holes to subsidize. So did the USA, but it had enough cash to
effectively subsidize them. The post-war USSR often did not. The PRC could have been a success story in terms of Soviet allies, but instead it broke away and that investment went down the drain. Thus, the USSR's bloc was weakened from the bat and we can see why the USA was aggressively "containing" it so the status quo would stay the same. Again, considering this, OTL's diplomatic situation of the USSR is quite an achievement. All of these examples accentuate the great potential of the USSR.
Of course, I am not saying that the USSR's own system did not cause problems. But what it does say is that these historical circumstances need to changed
as well to create a stronger USSR, particularly in the economic sphere.
My blueprint for a far stronger Soviet Union thus starts in the 20s. I could cheat and have a Menshevik-liberal Soviet Union, or have WW1 be far bloodier for the Western powers, or have the USA stay isolationist... but we need a recognisable Cold War. Therefore, a recognisable Soviet Union forms. My POD in the 20s focuses on Soviet agriculture. The USSR inherited rich land. However, for political reasons unwse agricultural policy (I'm looking at you, collectivisation) was followed, and this dealt a heavy blow to the agro-sector and had severe consequences for the development of the Soviet Union. The "deficit" in consumer goods that haunted the USSR included agricultural goods, and that was a large grievance people had with the regime. The importation of Canadian grain is a ridiculous situation which needs to be avoided. Agricultural exports would have saved the USSR from many troubles. Now, in my opinion, agricultural policy reform cannot involve economic reasons - those were thrown out the window for politics. Stalin knew that economically these policies did not work out. Thus, what really needs to be done is to have the 20s USSR stop fearing or ignoring peasants and using collectivisation as a political tool. Perhaps Stalin takes to simply purging instead of famines. The POD here is murky, but it requires getting Stalin to stop seeing collectivisation as useful. Maybe a better agricultural advisor or lobby. A stronger agricultural sector in the USSR means no famines that haunted the USSR, no deficits, no imports, and more food in people's mouths which takes off a major grievance that people had against the government. While it does take away workers from crash industrialisation, the stability it incurs will be worth it. (Don't look at modern Russia for the result, however - the agricultuiral sector is still suffering from the Soviet legacy and the problems of the 1990s on top of it all). No doubt in the 20s and 30s there will still be problems, but they will slowly but surely get ironed out since economic and political reasons drive the sector's development.
So that eliminates a major problem of the USSR, particularly in the post-war period. Falling apart is no longer on the cards without this major grievance. Let us say that Stalin changes little else aside from the agricultural sector. The purges are still there, and so on. We need to keep history and the USSR recognisable. Now we arrive at the 40s, and Hitler has taken over much of Europe. We need to avoid another catastrophe that the USSR suffered that underscored much of the post-war period: WW2.
My favorite way of dealing with that problem is by doing what many AH.Commers want Hitler to do: focus West in the 1940-1943 period. Hitler attempts Sealion, or Hitler focuses on the Meditterranean, or Spain allies with the Axis, or etc. This plays perfectly into Stalin's plans of letting the capitalists and fascists bleed each other white (unlike OTL in which the only nation not bled by the war was the USA). Hitler slowly saps his strength in the East, while Stalin builds up his armed forces. Then, sometime in 1942 or 1943 Stalin strikes: thousands of T-34s liberate Europe. The Germans may have known of the invasion but are simply outnumbered and Stalin shows the world a
real blitzkrieg. Within the year, Berlin falls and Stalin grabs at least all of Germany (France may be overstretch so we avoid that). He enters the Pacific War far earlier than OTL. Korea is unified under a Communist state (less paranoid due to no Korean war) and Japan has a large Soviet occupation zone.
The situation here is vastly better than OTL, so much that I think it
alone would be enough to make the USSR have thrice the GDP of OTL. First and foremost, the USSR was never occupied and never had such huge casualties. 20 million of the population is not dead, and we also avoid the gender gap that haunts the USSR to this day. The USSR does not lose anywhere from a third to half its industry (if not more) to German occupation. Its railway network is not cut up by retreating German forces. Its cities are not bombed aside from maybe a few lucky raids by the Luftwaffe before it completely overwhelmed in the first days of the air campaign. No rebuilding is required (this sucked up Soviet GDP and capital for a long time after the war). The USSR has far more capital to throw around at ...well, everything, and is never forced to concentrate its economy on the Cold War and cut out consumer goods completely (which the USSR either couldn't make because it was unindustrialised in the 20s and 30s, fighting a war and rebuilding in the 40s, or in the late 60s onwards fighting the Cold War - note I leave out the 50s and 60s, which did see consumer goods being available in at least some form).
The USSR also receives a sphere of infuence in the Cold War which is better due to several factors. First, it is larger, but not the type of "larger" which means lots of money holes in which capital enters and is never seen again. Not only that, but its sphere of influence is not AS ruined by warfare. Germany isn't as completely bombed out and neither is Korea (though this one is due to the Korean War in OTL) or Japan. Eastern Europe, though looted by the Nazis, was looted less. So the USSR doesn't have to waste capital rebuilding THESE states on top of itself as in OTL. Well, it does, but not as much as in OTL. It also doesn't have to take any industry as spoils of war because its own industry is intact. Plus, all of Germany's scientific and industrial talent is now available to the USSR, except for those that managed to flee. This denies said scientists from being useful to America, too. So this is a sphere of influence that can provide some actual economic benefit and trade to the USSR. Indeed, that may cause the alt-Warsaw Pact to be slightly less Soviet puppets and slightly more Soviet allies.
The changes that take place after the war in the USSR do not require their own POD but follow from the vast changes made by this timeline already. There is far less economic scarcity, no post-war famines, or anything like that since the agricultural sector is untouched by collectivisation or the war. Stalin also does not have the prestige of saving the USSR - he saved Eastern Europe and the world, of course, but it wasn't a life or death struggle. The USSR's prosperity also makes Stalin's harsh methods seem more questionable. The lack of such a WW2 lessens the power of OTL's conservative faction in Soviet politics considerably, as well as the military. Thus, when Stalin dies I see reformists and the "young guard" of liberal
komsomol members taking power more strongly in their reins, criticising Stalin more strongly, and with a stronger focus on "providing for the people" and such. As said, liberals. Stalin is thus seen a sort of abberration of totalitarianism as opposed to Lenin's
true successors in the 50s.
Economic reforms in the USSR cannot, however, be simply copying OTL China, particularly in this environment. The USSR does not have billions of workers able to flood the capitalist markets (which it has no reason to enter, anyways), it has a highly skilled base of educated workers and industry instead. So reforms will be less "complete capitalism with the party in control" and more third way-ish, especially the type of scarcity suffered in OTL isn't there to completely destroy faith in Communism. Reforms would focus on allowing small-scale commerce, perhaps looking at NEP for further emphasis on the whole "we are Lenin's successors" line that would be touted. The industial sector would go from being purely heavy industry and "factory giant" to smaller scale factories producing goods, though these factory giants would be retained - the USSR still has use for super-heavy industry such as in the mineral sector and so on. The enlarged Warsaw Pact could form a somewhat self-sufficient economy, particularly with Germany involved as a second heavyweight. By 1970, the GDP of this USSR would be far higher than OTL and would likely seriously challenge the USA if not overtake it (once we engineer problems for the USA).
There we have a far stronger USSR. Collapse is not on the cards, and socialism seems to work once it is divorced from Stalinism. If I wrote the timeline I would probably see the Cold War "end" on multi-polar note, with both contestants retiring from hostility and preferring to cultivate a friendlier rivalry and powers like China and India emerging. However, the requirement is "victory" like in OTL. So we need further changes, and have the USA slide into isolationism (though still as one of the Great Powers, along with the USSR and the developing countries).
The Cold War starts after WW2. The USSR is even bigger and scarier (and seemingly waltzed in to take the lion's share of the spoils in the middle of the war), so the Red Scare is magnified too leading to a more right-wing USA. The USSR has more money and influence, and an actual trading bloc to boot, so it makes more and better allies instead of dictators who want Soviet subsidies only. The USA is unable to "contain" the USSR and starts taking a hard line against all socialists (such as Western Europe) and third-way countries, moderates or not. I'm thinking it invades Indochina in full, leading to a large war that drags on there. The PRC bristles at American military buildup in Indochina and Taiwan and, while independent, stays at least somewhat warm with the USSR. The USA has greater race problems (the one item everyone seems to agree on), and mega-Vietnam, messes around too much in Latin America (no Castro, however - the USSR backs moderates and populist lefties instead), and then intervenes in the Middle East (and fails, again). A massive economic crisis results as oil prices go up. Perhaps they even go to the USSR for oil, a sort of reversal of OTL's Canadian grain embarassment. Western Europe is greatly annoyed by American failures and starts thinking about peaceful coexistence with the USSR instead of the policy of constant hostility that the US pushes. America loses more and more cash on propping up right-wing dictators. The Cold War, instead of being OTL's hard-left Communism vs. moderates and right-wingers is redefined as right-wingers vs. moderate leftists. The USA is nowhere near collapsing, but after Western Europe elects some socialists who push peaceful co-existence and welfare regimes the USA goes into crisis of confidence. Finally, the American political establishment tires of "containing" the USSR and pushes friendly relations while possibly withdrawing from some countries. Since before, America had an aggressive and hostile attitude, this is painted as a "victory" for the USSR (which has grown more liberal/moderate over the years - a big question is how much does it do so). America is intact, but is not the top dog. The USSR isn't exactly the hyperpower, but it gets "top dog" status for a few years due to no one else really challenging it. China and India rise as powers, the USA recovers as a firmly capitalist but no longer interventionist power, and the USSR keeps the Warsaw Pact around but notes that it is far less homogenous than before.
Now, there are some holes that we need to patch up but the above is the bare skeleton of such a timeline. It can be summed up as: The USSR is far stronger economically (better agricultural policy and untouched by WW2), becomes more moderate as a result, US becomes firmly right-wing and "loses" by being more aggressive than OTL and then stepping back to peaceful coexistence.