I'll expand a little bit my "oracolar" comment above (with less fun) :
They have studied physics and mathematics, and physics and mathematics, and ...
There was "explorations" of "outer layers" of atmosphere with balloons.
There ware the "experiments" made with rockets (mainly German) used during WW II.
But mainly, there were faith in the immense power of newtonian mechanics (and mathematics) to predict the correct behaviour of bodies subject to the "law of motion".
With insight, space travel (think about a 10 years travel of a little "spacecraft" able to "land" on a comet after a journey of millions of km) has been - for me - the "paradigmatic" cased of verification (if any) of a scientific theory.
I mean : we can speculate about skepticism, philosophical realism and any other kind of "mental experiment" about the reality of the world "out there".
But, if we are able to compute a ten years long trajcetory with this precision... this means that the theory is definitively correct.
See e.g.
If you can spray them, then they are real.