I realise this is a trite observation, but it never ceases to amaze me that it took just 22 years from the beginning of space exploration to walking on the moon.
The delta-v from Earth Surface to Low Earth Orbit (beginning of space exploration) is 9km/s. The delta-v from Earth Surface to Moon is 15km/s. So basically once you learned to go to space, going to the Moon is "only" 60% harder, even thought the moon is 1000x further away.
1. Walking on the moon implied a return trip which requires an extra ~3km/s.
2. Under the rocket equation the fuel requirements for more delta v grows superlinearly, which then awkwardly makes your rocket bigger, which requires more fuel...
3. 22 years prior a metal can went to space. The scale of a manned moon mission in comparison is absolutely nuts, even basic things like having rocket motors that can be relit is a large technical challenge.