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Go back to 1911 and convince Taft to concede the Republican nomination to Roosevelt. That allows Roosevelt to stomp Wilson, get the US into the war before Russia left, and get the war over with years earlier.
This prevents both Stalin and Hitler from rising to power, and prevents most of the European theater of WW2, as well as a host of other knock-on effects.
In this scenario Lenin does not manage to take over Russia and the warning to the world by the real life examples of Germany and Italy about the dangers of fashism does not happen either. Authoritarianism raises its ugly head later in a world with better weapons and more destructive potential for humanity.
Would that prevent the space race?
I doubt it. The Russians are still gonna want to try to beat the US at anything they can, and prove themselves on the global stage, but it may have been a cooperative venture, instead of competitive.
Interesting take.