I'll admit up front that pre-1900 is more my haunt, but a thread like this is always fun, and I'll take a stab at it. One note in advance: it's pretty clear to me that in post-1900, more than in pre-1900, lots of discussions like this one soon go into very detailed discussions about exact amounts of oil reserves, how many vehicles each side had, the number of bullets they had, the quality of their tires, even...! And that makes sense, since post-1900 we often have more accurate insights into such numbers.
But does that not often lead to a sort of "not seeing the forest for the trees" problem? Everybody has argued about Barbarossa's specifics very often, and it's happening again. Eveyobody has mentioned that Nazi germany can't win when fighting three global powers at once. The simple numbers mean victory is outright impossible.
Nobody has mentioned that such a situation could be avoided early on. I refer, of course, to the Dunkirk evacuation. And I wonder why nobody has mentioned it yet. They evacuated 338,226 soldiers there. They evacuated pretty much the entirety of Britain's army at he time. And they managed it because the Germans tarried. The Germans didn't have to tarry. I'll admit right away that such a indecisive fuck-up, caused by differences of opinion and clashing egos, is characteristic of Nazi (mis)rule, but an ATl where Hitler barks "March in there right away and take them all prisoner-- kill those who try to resist!" is hardly impossible.
And what then? Those poor boys stuck on the shore don't stand a chance. Resistance to the last man? Over 338,000 corpses? Highly unlikely. Some will resist and die, and then... surrender. It's the only viable option.
And then Hitler has some 338,000 POWs. He has Britain's army held hostage. Well, for starters, Churchill's political career is over. He was heavily doubted right at the start. Halifax was expected to step in. Negotiations (via Mussolini) were already being prepared for. The miracle of Dunkirk turned everything around. If there is instead a disaster of Dunkirk, then that is the end. Churchill is out. Halifax is in. Halifax, who was already prepared to negotiate at that point. And now Hitler has 338,000 negotiating chips. So negotiation begins, and Hitler says: "Your boys will be our guests. They will be treated well. Fed well. Cared for. And in a few years, they come home, fatter than they were. Unless you try to stab us in the back. If you do that, only their heads come home."
What Prime Minister is going to be the man who makes the decision that leads to 338,000 boxes being delived to Britain? That's... political suicide. No administration could possibly survive that. So as of this moment, it's "Do what that nice Mister Hitler says, and make sure he knows we're still his friends." This means that Hitler can at once draw away virtually all his defensive forces in the West, and re-dedicate them to service in his future campaign in the East. It also means oil is no longer a problem. The British empire has oil, and will provide it to that nice Mister Hitler on the cheap. That wil be one of the conditions for him taking such good care of his... guests. (And Hitler can surely go all "carrot and stick" here. Say to them: "In return for your compliance, we will make France hand over all its colonies except those on the North African coast to Britain." That's completely meaningless to Hitler, and it looks like a big win for the British Empire. Sure, Hitler rules the continent, but Britain rules the waves! We still matter, lads! This deal isn't a humiliation after all! Takes the edge off a bit...)
With no need to make a play for the USSR's oil fields just to have a chance, Hitler can go with the original plan without hesitation or delay: drive for Moscow. Stab at it. Far more than in 1812, taking Moscow is a crucial victory. Even if Stalin burns it behind him, that's no matter at all. Moscow is the rail hub for European Russia. If you take it from them, that is a huge blow to them. And under these circumstances, Hitler can take Moscow. Don't forget that they reached the city's outskirts in OTL. Stalin was literally weighing his options with his evacuation train at the ready. In the ATL, he has to get on that train.
Does that make it a sure thing? Not at all. But Hitler could win, given these conditions. He very well might.
And of course there are other considerations. Hitler knows that with Britain out of the way, the clash with the USSR is coming. And it'll have to be soon. Stalin was absurdly trusting towards Hitler (which is truly weird, considering his usual paranoia). He kept up his side of their agreement (sending supplies to Germany!) even when it was becoming clear that Hitler was about to attack the USSR. Stalin was warned, and dismissed the warnings. I think that, since Hitler's treachery was obvious in OTL but Stalin refused to recognise it, he'll act in the same way in this ATL. (His strange blind spot is, after all, not magically erased). But Hitler will know that he has to act quickly. This may cause two further oft-discussed changes:
1. Hitler may strongly urge Japan to forego their Pacific designs, and launch an attack on the Russian Far East instead, timed to co-incide with Barbarossa. This is credible, because the Japanese asked his opinion on it in OTL, and his reply was basically (in typical Hitler fashion) "Whatever, do what you want." Now, of course, the Japanese preferred the Pacific strategy, but that was in large part because they -- also -- had no damned oil! And in this ATL, Hitler can tell Britain to sell Japan oil. (Again, part of the deal...) This solves Japan's problem, and will realistically get Japan to agree to a "USSR first" strategy.
2. Since Hitler is in a hurry, and knows that he can't get distracted, he'll impress that upon his allies, too. As in: "No bullshitting around now, I need everyone you can spare for the crusade against the communist menace!" So when Mussolini starts talking about invading Greece, Hitler directly tells him not to do that. Russia first. Afterwards, he promises, Benny can have a whole lot of German Panzer to roll all over South-Eastern Europe. (Also, those French North African colonies Britain didn't get? They're for you, Benny. Say it with me-- Restored. Roman. Empire.)
...And those two changes avert a minor delay for Barbarossa, and give Stalin another front in the Far East. Now, before anyone says it: I know that the German intervention in Greece didn't really delay Barbarossa by weeks and weeks, as some believe. But it did delay a bit, and with the autumn rains coming around the time when you reach Moscow, literally every day counts. Also, the adventure in the Balkans and Greece diverted men and materiel that couldn't be deployed against Russia on time as planned, so avoiding that is also a plus. Additionally, I know that anything the Japanese do in the far East is only going to be a distraction to Stalin, rather than a substantial threat. But in a fight for survival, a distraction can have critical consequences...
I firmly believe that the above is not an unlikely scenario. It is certainly not a given, but the two projected "additional benefits", if added to the original POD, tip the odds in Germany's favour. I see Stalin retreating beyond the Urals, and European Russia being taken by the Nazis. That gives the Nazis their own oil supply, at which point relations with Britain can be normalised. Mussolini gets his North African possessions and German help in becoming hegemon of the Balkans and Greece. Germany has its Lebensraum, and is basically done. Britain gets its soldiers back, and can call it "peace with honour". Japan has some more of the Far East, and can consolidate the empire it has. The USA never even gets involved.
Is this the end of the story? Of course not. Hitler was a lunatic who wanted to conquer the world. Before long, he'd be planning for new conquests. Also, Nazi economics were a house of cards, and would eventually demand a new injection of plunder to make up the gaping deficits. That, too, would encourage new wars of conquest. On the other side, Britain, now free of Hitler's hold, will silently start to prep for a re-match. In the end, I think a third world war is likely, and I think the Nazis will lose it by way of a few mushroom clouds. But that's world war three. We're talking here about world war two, and I have outlined here a way in which I believe they could have won it.