The moon landings were practical science at its best. Computer technology, rocket technology, and mathematics were used and/or developed to accomplish a goal. Our understandings of conditions outside of our planet were tested and we learned that the moon was not made of cheese and was very much like what we already knew about our own planet.
Magical thinking can be used to convince people of many strange things whether it be modern faith healing, wild conspiracy theories about things like faking the moon landing, or the strong belief in modern physics and its theoretical guesswork about how the universe was created. I believe intuitively that the moon landings occurred because I followed them and lived in that time period. Admittedly, I did not go to the moon and have no physical proof. But proof of the moon landings is a whole lot easier to understand than hypothetical guesswork about how our universe was formed. Sometimes there is a point where preponderance of supporting evidence or the lack of legitimate conflicting evidence makes certain assertions correct as historical fact. This is easier to do in time periods that are recent rather than billions of years ago. And it helps to actually be there to see or do it.
How could one believe a person were not born as a result of the mating of two humans (most likely to be the people professed to be our parents) rather than resulting from a magical occurrence? Perhaps an alternative scientific hypothesis might be that we were individually placed on the earth by aliens. Then there is the supernatural explanation likened to be a possible by many of, say, a virgin birth. Finally we could very possibly be the result of an alternate scientific process whether it be a more likely scientific possibility like cloning or a fairly unlikely scientific explanation that we could have been sent back in time by future scientists.
There is really no way to prove even the most basic of events beyond all doubt.
That said, I take it on logic and faith that the moon landings did indeed occur and I like this video: