I doubt that “we” went to the moon. First of all, very few frum Yidden would ever have “the right stuff” (heck, it is almost impossible for a frum Yid to serve in the American armed forces in any capacity), and there is no way one could be an astronaut even with the more absurd “modern” Orthodox heterim (remember there would no heter for training activites on Shabbos).
Furthermore, if the moon is in fact made of cheese, it would pose serious kashrus issues.