I think there's some merit in what you say, but it wasn't the space race per se, if we mean Project Apollo and such, it was nuclear weapons and the V-2, because those happened in 1945 and the Space Race got started later (and for that matter, a significant motivation in the Space Race was the fear of The Best And The Brightest that Soviet missile technology would surpass the USAF as a strategic threat multiplier).
It's no coincidence this was signed the year after Sputnik, but the fear of Sputnik wasn't fear that the Soviets would win civilian gold medals in space, plant the red flag on the Moon first, it was fear of Soviet missiles -- if they could put a dog into orbitt they could certainly land a 1Mt nuke on Miami -- and indeed the notorious "missile gap" helped JFK defeat Eisenhower's VP two years later.
I think there's some merit in what you say, but it wasn't the space race per se, if we mean Project Apollo and such, it was nuclear weapons and the V-2, because those happened in 1945 and the Space Race got started later (and for that matter, a significant motivation in the Space Race was the fear of The Best And The Brightest that Soviet missile technology would surpass the USAF as a strategic threat multiplier).
For example: https://en.wikipedia.org/wiki/National_Defense_Education_Act
It's no coincidence this was signed the year after Sputnik, but the fear of Sputnik wasn't fear that the Soviets would win civilian gold medals in space, plant the red flag on the Moon first, it was fear of Soviet missiles -- if they could put a dog into orbitt they could certainly land a 1Mt nuke on Miami -- and indeed the notorious "missile gap" helped JFK defeat Eisenhower's VP two years later.