You need to read “One Giant Leap: The Impossible Mission that Flew Us to the Moon” by Charles Fishman. Fascinating account about the entire process of the moon mission.
As for the computers, it tells how a bunch of middle-aged and older seamstresses SEWED metallic disks into fabric and connected them with conductors to create the programs for running the Command and Lunar Modules. One mistake, and you start over! No backspace key available... Those were the logic circuits. Not really software, more like firmware, I guess.
It is really a great book IMO. I was 9 when we landed and the moon shots got me into engineering. I worked on ICBM’s for a time as a young engineer.
Take a closer look at the lunar and command module computers.
It is not what you think it is:
https://www.aulis.com/pascal.htm
https://www.aulis.com/pascal2.htm
Did our astronauts navigate to the moon using the stars, as NASA said?
I’ve read a few. There was a lot of wild stuff. They were right at the edge of technical possibility. They were making the technology to get that edge. Kinda crazy. And awe inspiring. Which is why I despise all landing deniers. They’re scum.