Slide rules and ingenuity. Kinda like the guys who brought apollo 13 back home.
The father of a close friend of mine was a design engineer with Lockheed back in the 60's. He's in his mid 80's now, still uses a slide rule and hates calculators....
I worked in Hollywood, CA, selling video equip in the 80’s. One of my clients was Lockheed in Burbank (the industrials used far, far more gear than the studios, at least as far as them buying it from anyone other than direct from the mfrs) Burbank = just over the hill from Hwd. Burbank then was a very cool, quirky little town, with gazillions of weird but fascinating ancillary businesses that supported Lockheed and the studios.
Once I was taken on a tour of one of Lockheeds’ design facilities. It was kind of cool, of course, but I felt bad because while I was there, every computer screen (this was the mid-80’s not the 60’s like you said in your post) was flashing “uncleared visitor” and there were probably 50 qty 80K/year engineers and geeks sitting around in cubicles unable to get any work done.