I'm extremely skeptical the Soviets taking the actual time to prepare benefits the Finns more then the Soviets, given that the Soviets can commit proportionally much more massive resources then the Finns could ever hope to acquire. As it was, the Finns did acquire all the stuff DrakonFin talked about and even more from captured Soviet stocks from those first disastrous months… yet when the Soviets stopped dicking around with non-existant preparation, ditched the overcomplicated maneuver schemes, and brought up the appropriately equipped and trained troops, they managed to brute force the Mannerheim line after almost two months of attritional skirmishing to wear the Finns down followed by a week of all-out assault.
A few months of extra time would increase the Finnish readiness for war pretty much automatically, the Finnish military leaders and politicians in the fall of 1939 being in agreement that immediate defence purchases would be necessary. Which they were: Turku, the city that became the premier trade port of Finland during Winter War IOTL, started the war with only three batteries of AA machine guns as the only active AA defence of the city, the shipyard and the port. The field artillery would use 1870s vintage artillery pieces. The Vickers 6-ton tanks the army had didn't have guns installed in their turrets. The first line fighter force of functional planes was made of thirty-three Fokker D.XXIs and ten Bristol Bulldogs. The list goes on. In these conditions every month of new acquisitions for the military will make significant improvements to the Finnish readiness for fighting a war for survival. IOTL, when the Finnish forces took new weapons and materiel in use during the war, they had to do this in conditions where the great majority of all trained personnel was engaged in wartime roles. If they could instead introduce this new equipment in peace-time conditions, albeit with increased readiness, this process would be easier and faster. Only a very small part of the weapons and equipment captured during the Winter War was used in that war, and most would only be used in the Continuation War: in the event, there was scarcely enough time and resources available to collect, fix, and field these captured goods during the short conflict.
Now, for the Soviets the question is not just time, but also the military and political leadership making the decision that Finland is a serious enemy, not a pushover. Not only would Zhukov have to understand this, he would also have to convince Stalin to give him his support for using significantly more resources and troops for the Finnish campaign that he had originally slated for the invasion. If this happens, if the Soviet leadership understands that Finland is not a military nonentity that will cave in after the Red Army kicks in the door, then giving the Soviets some months more time will probably work in the attackers' favour - just because of the huge disparity between the resources Finland and the USSR can commit to the fight. But just time alone will not help the Soviets to the extent it would help the Finns: if there is no joint understanding in the Soviet leadership about Finland being a serious adversary (more than "White militia" stuck in 1918 patterns of thought, strategy and tactics, with pro-German officers lording it over a mass of recalcitrant conscripts who will revolt or abandon their posts soon after the war begins), then some months of additional time will not fix the basic problem behind the Red Army's failure IOTL. Which was underestimating the enemy.
I agree
What are the least difficult ties of the year to invade Finland by the way?
From early June to mid-September. This avoids the problems of winter and rasputitsa, and allows the Soviet naval superiority to be used for the best advantage. Invading in the summer would bring some additional challenges for the Soviets, too. On the Karelian isthmus and north of the Ladoga the lakes and various swamps and marshes would be a bigger obstacle when they are not iced over. Generally, a Soviet invasion of Finland in the summer of 1940 would probably look like a mix between the OTL Winter War and the fighting of the summer of 1944. Both sides would in this scenario be stronger than in 1939 but weaker and not as effective as in 1944. Looking at these two OTL examples, I'd say that unless the Red Army here can somehow draw Finnish strength into secondary sub-fronts (like I mentioned above, for example with amphibious landings), then they will still have to use a lot of troops and put in a significant effort to smash through the Finnish defences on the isthmus and in southern Karelia. Assuming some real preparations by the Soviets to fight a real enemy in an actual war, this would probably take them from four to eight weeks, depending on various things on both sides. Eventually, the Finns would lose. The question is how long they can keep up a coherent front, and what political developments happen in the surrounding world: will they get outside help like IOTL (the Allied plans of intervention convincing Stalin to wrap up the war) or not? If not, Finland will fall and be occupied by the Red Army within two to three months from the beginning of the main Soviet attack.
The thing is, like I have said before, whether the Red Army uses four weeks or two months to get from the 1920 border to Helsinki, the war would still not make the Soviet Union look good in military terms. Like the OTL contemporary views of the war outside Finland show, in 1939-40 almost everyone saw Finland as a military midget and the USSR as a major, if not a great power. Given these expectations that practically,
structurally make politicians, soldiers and the general public in Europe and America underestimate the difficulties the Soviets would have in invading Finland, I think that it is pretty much impossible that the world in general would not see the war as a Soviet failure, at least to some extent, even if they manage to wrap up the conquest of Finland in the smallest realistic number of weeks.