Heck the USSR put a rover on the moon and pulled off a sample return mission, so they know the mechanics of how its done and know the Americans could and did put men there.
If their N-1 moon rocket wasn't such a miserable failure, they would have also had the horsepower to go beyond the unmanned stuff and put a cosmonaut on the moon (or at least kill a few trying).
The history of the Russian N-1 was pretty interesting. It was a battle of egos between two high-level appartchiks that sunk the Soviet moon program. I don’t recall the details, but I remember shaking my head at how stupid and petty it all was.