[assuming a POD or more in the beginning of the 20th century] I would argue the opposite, that the world wars had stunted aero & rocketry tech significantly, and if the first half of the 20th century was the same great power games as the latter half of the 19th century (i.e. mostly peaceful in the core, and most conflicts being fought elsewhere with relatively low stakes) there would be more, rather than less, advancements in technologies. The broken window fallacy is a fallacy for a reason, and all the trillions of bucks and tens of millions of lives lost in the world wars (and the revolutions due to said world wars) has made the world a poorer place.
I detailed my thoughts on how aeronautical and space technology would develop in a world without the World Wars
here, and in short, I definitely agree that a multipolar world would likely see a longer and more advanced space race, if developing along different technological lines than OTL. There was a lot of competition between the great powers in arms, technology, and prestige before WW1, and those would continue in a world where that geopolitical situation continues.
In a way, while the Cold War of OTL was good for space development in a lot of ways (having two rival and ideologically opposed superpowers competing for prestige and technology), I think it was still far from the best version of the 20th century for it. It was probably better than, say, a unipolar world (perhaps one where the USSR is defeated by Nazi Germany, which then loses to the Western Allies), where a single superpower has no competition, or a world where more than one superpower or great powers get along well (I sketched out a rough timeline for a world where all great powers are functional democracies by 1950 and couldn't really imagine them having anything to seriously fight over). But there were some disadvantages OTL had; while there was a Cold War, the superpowers were still at least on speaking terms and could hash out agreements, which brought the Outer Space Treaty and various nuclear and conventional arms treaties. These weren't bad things, but they did, among other things, kill the Orion project, resulted in very little impetus for military development of space, and prevented anyone from claiming territory. And the Cold War did end in OTL, causing the end of the Buran, Mir, Space Station Freedom, and other things.
If the Cold War had been more antagonistic, then competition in both military and scientific development in space could have been more intense.
This map and linked TL shows a world where a more intense Cold War leads to a military arms race in space (culminating in a Soviet government-in-exile after its collapse occupying their orbital missile platforms and refusing to recognize the new Russian government). To turn the dial up even more, imagine perhaps an Axis victory, with the US-led Western Allies standing off against a Nazi-led Europe that defeated the Soviets. Such a cold war would likely be
far more intense than the OTL one, where the two are unlikely to ever agree to any treaties, be it arms reductions, bans on nuclear weapons in space, or on claiming territory on celestial bodies. Against a rogue state that's a superpower (and who likely has a head start on rocketry compared to the OTL Soviets), the Allies would have no choice but to go all-in on space and carve out and protect their place in it, because there's nothing else stopping their enemies from doing what they want up there.