During the entire "space race" the URSS had been, as you know, quite in advance in respect to the US as far as any "milestone" was concerned. Something like 18 - 24 months in advance. They had a "man on Moon" project, too. When they measured the amount of radiation in the Van Allen Belt(s) they found out that in order to protect the astronauts (or the cosmonauts as the USSR called them) a huge amount of shielding was needed, something like 1 metre thickness of lead. That made the goal impossible to be attained. So the USSR scrapped the project entirely as infeasible.
Either the Van Allen belt makes some favouritism, or the Apollo missions never brought any man on the moon (as they came back).
USSR propaganda always said it was all a big lie. Still nowadays in the former USSR states the majority of people do not believe that the US sent men to the moon. Americans believe it because US propaganda says it. US propaganda also says that the USSR "would be only happy to expose the fraud". The USSR exposed the fraud but you weren't listening
After scrapping their moon project the USSR begun working on something that could be done, the space station Mir (Peace) which lasted in the space for a very long time before being replaced by the ISS which is, in fact, heavily based on the Mir project.
The ISS, like all manned Space Shuttle missions, remains "near" the Earth, the Van Allen belts are further between earth and moon. The only manned space missions which supposedly have passed through the van Allen belt are the Apollo missions. Recently the NASA scrapped projects for a second series of manned missions to the moon citing "higher than expected radiations" in the Van Allen belts. The stuff is there since billions years. Go figure.
Besides, there are plenty of proofs about existence and working conditions of the ISS. The space agencies involved did not systematically destroy everything that could be claimed as proof, and could be exposed as a fabricated fake. This cannot be said for the Apollo missions.
Dig the internet and you'll discover plenty interesting stuff...
As a further point of reflection I would ask you why do you think that the USSR wouldn't have sent men to the moon. Even if the US had passed the USSR during the race, wouldn't have been rational for the USSR to continue racing and arrive not distant second? The US had arrived distant second at ALL the previous milestones. The USSR would have suffered little loss of pride by sending their mission to the moon maybe some months after the US. So why do you think they did not do it? Why did they just "give up" entirely the race with the US? Isn't that strange?
Consider that the Soviets arrived first to the moon with an un-manned mission, were the first to bring back to Earth some moon stones, and were generally "well positioned" so to speak