There was certainly a lot of interest post WW2. IIRC, Russia was ahead in rocketry pre WW2., but the Germans caught up and then once the Americans figured out how to launch their 'acquired' Nazi weapons.. with the help of their acquired Nazi scientists.. it all took off. as it were.. I recall being fascinated by things like 'edge of space' balloon ascents and parachute drops. Bell X1/X15.. Chuck Yeager, 'The Right Stuff', 'Sputnik' Telstar, Earlybird. The Friendship, Mercury, Gemini, Apollo and Space Shuttle programmes.. etc., etc.
They were exciting times.
It's also easy to forget that there was a whole parallel military effort around intercontinental ballistic missiles cruise missiles etc. The 'Space Race' was the acceptable face of the Arms Race.
Around 1970, I read a fascinating book by some American military chap, who gave a warts and all, very detailed account of the American antics with captured V2 rockets etc. They really didn't have much of a clue at that stage and I suspect that only the sheer weight of resources.. plus Von Braun.. gave them the eventual edge.