Anatoly Zak has an interesting and detailed article at the BBC on the origins of the German rocket program in the 1930's. This was a military program that ultimately lead to the V-1 and V-2 rockets used against Britain in the second world war, although the factories that made the weapons were staffed with slave labor. (For documentray lovers, The Reich Underground [Netflix] shows the underground Nazi rocket factories such as Mittelwerk -- ~20,000 concentration camp inmates were killed in forced labor at Mittelwork alone.)
Later the victorious Allies collected all the German rocket engineers they could get their hands on and put them back to work, so sadly the successes of the US and Russian space programs owe much to this tainted knowledge.
This is not to say that home grown efforts on rocket propulsion by people like Goddard in the US and Korolev in the USSR were not significant - merely that the Germans devoted significantly more state funding to developing practical military rocketry than the US and USSR of that period did.
[Both images are WWII-era photos of the underground V2 factories at Mittelwerk, Nordhausen, taken from Geoff Walden's fascinating "Third Reich in Ruins" site.]