The greatest proof we have that the United States was the First Nation to land a man on the moon and did so in July of 1969 is that their primary geopolitical enemy had beaten them at every previous step in the space race and didn’t contest it. If there was a chance that any aspect of it was faked the USSR would’ve used it as propaganda and a cudgel. Instead they confirmed the moon landing. It may be hard for some people to believe we set foot on the moon, but it’s much harder to believe the ussr covered America’s ass on this one.
It’s actually the same basic evidence that we have that Yuri Gagarin was the first human to go into outer space alive and return alive. If it hadn’t happened the United States would’ve contested it.