That really depends on where you consider the "finish line" to be? Is it the Moon, Mars, Venus?

The Soviets have done things in space that the US has not, like sending a probe to Venus. That's why I bring up my first point. The Soviets were also the first to land a probe on Mars. The US has also done things the Soviets have not, like sending a man to the moon. So where do we define the end point for the "space race"?

When it comes to contributions to the body of international science, putting space stations in the air and putting rovers on planets are a lot more important than the propaganda victory of a spacewalk. A person doing a spacewalk on the moon isn't even as efficient at collecting mineral and soil samples as a rover would be. It's also kinda irresponsible since it puts lives at higher risk than just doing standard space missions.

At the end of the day though, this is just a communist shitpost. Science has always been international collaboration and not a national chauvinist thing. Communists are the first to acknowledge that since communism is an internationalist ideology that upholds the working class.

No one besides the US wanted to put a man on the moon, because it was a pointless and dangerous stunt.