This is the biggest problem. A totalitarian system will breed Lysenkoism, and eventually science will suffer for it.Take a look at this, and tell me how it's possible for the Soviets to either get ahead, or if they do, to remain there. Hitler may have been worse with the sciences he refused to tolerate, but Stalin and his successors sure weren't open to some ideas.
The soviets were indeed ahead in the Space Race and it wasn't until the Mariners that the NASA began to beat them in their own ground (the USSR had been very successful sending probes to Venus, but the Mars ones were a string of failures). The US simply would advance much faster whenever they would set themselves to it.
I can only see a choice, that is probably so slim that is not realistic:
What if the space race had advanced much slower than IOTL, so much that the Soviet advancements were not seen as a strategical threat for the US. The US would be simply content to be able to place stuff in orbit to nullify the strategical advantage, and would not engage in a space race.
Also, another requirement might be a successful Perestroika that would transform the USSR into a non-totalitarian but not-completely-democratic state, with an economic system closer to the Swedish socialism. Very unlikely, i know, but if this happened, certainly the USSR would have been able to keep any scientific advantage on the space that it had managed to still have.
So: no space race + successful perestroika