@AliBaBa
Unless you witness something yourself, then *nothing* can be proved to be real ... and given that some people claim to have personally witnessed UFOs, and the Statue of Liberty disappearing on that magic show ... nothing can be 100% proved to be real.
So we apply logic, common sense and rules. We find people we trust to report accurately what they experienced, we look at video tapes and photographs, we analyse things to see if they make sense based on the "rules" that the physical world appears to follow, and we decide whether to believe government statistics, doctors' diagnoses, lecturers at college etc. And very importantly we test things to see if we can find counter-evidence to disprove each particular "fact" or assertion. And if there is a lot of good quality supporting evidence and nothing credible to prove the opposite, then we accept things as most likely true. Whether it is the maximum dose on medicine or the maximum load on a bridge.
I didn't walk on the moon, but the various bits of evidence around support that as being possible and very likely, and the counter arguments that I've seen have either been shown to be false/invalid or are misinterpretations or distortions of the "facts/evidence".
So I believe man walked on the moon, that the sun will rise tomorrow and that Tottenham Hotspur didn't win the FA cup last year.
"plenty of good counter arguments against the very escapade from taking place" - where? I'm intrigued, can you point me/us at some of these "good counter arguments"?
"There's no good proof that it happened" - aside from personal testimony, photographs, videos, echos from corner reflectors placed on the landing site, appropriate direction and distance radio signals picked up from many places across the globe triangulating to the correct place, many thousands of people involved in putting the missions together, and moon rock brought back. I'm sure I'm missing a few other bits.