Those NASA scientists used the biggest computers they could so that they could make the smallest computers they could.
Here's what state-of-the-art computer technology looked like in the 1960s:
https://en.wikipedia.org/wiki/Apollo_Guidance_Computer
(In 2019, I was lucky enough to help out on a restoration project to celebrate the 50th anniversary of the first Moon landing. I designed a PCB that attached to the AGC's spacecraft connector. Afterward, I also got to meet Margaret Hamilton, who is pictured on the wiki page.)

