Spotty logic. You have doubts because technology 50 years ago was lesser than technology now. You have to ask yourself why wouldn't the Apollo computer be capable of doing what it did. You're basically ignorant on the matter.
The Apollo flight computer was demonstrably capable. Anyone can verify this by using one of the simulators.
This was quite literally the first personal computer, predating dos, Linus, anything like windows or OS X.
https://en.wikipedia.org/wiki/Apollo_Guidance_ComputerYour ability to type these messages online is the result of Apollo.
What you are really trying to say is, NASA mooned us all, right?

Actually, no. Like any government agency, NASA can do little or nothing by itself. The work and the creativity, with rare exceptions, is the result of contractors who seldom get credit.
Over a half million Americans worked in getting the Apollo program to succeed. They remain largely nameless, and the government and its agency takes credit.
At least, that's true when taking a superficial look.