The biggest proof has already been stated:
The Russians and Americans both wanted to win.
If the Americans HADN'T LANDED ON THE MOON, every Russian Scientist would have made a comment, IE, NO YOU DIDN'T.
So unless you believe yourself to be smarter than the American scientists who DID send men to the moon, AND the Russian scientists who couldn't find a falisy in their claims, with all their Satellites and sensors and whatnot, be quiet.
I posted a link that refutes every argument against it with HARD SCIENCE. Read it. Read it again. That's right. They ARE smarter than you.