Subsonic flight is a lot less demanding than supersonic flight, for one. The airplanes just did a lot less. They didn't fly as high, or as fast. They didn't carry radar, or infrared or missiles, just some guns.
I think a lot of processes exist today as a result of the weird failures that a 143-day development cycle entails. Stability and weight problems were pretty typical, and that's why they built prototypes and were willing to make modifications between development and production models.
The engineers had a grasp of the theory of stability, aerodynamics, propulsion, etc, but the difficulty of calculating things meant that a lot of cut-n-try was allowed. Electronic computers have caused numerical analyses to be much more accurate and complete, but those analyses take time and the effort of specialists.
Engineers were more plentiful. They only had subsonic flight to deal with, so there wasn't that much to learn about. Model airplanes had been hugely popular since the 20s, so there were lots of guys with hands-on experience with subsonic flight, albeit at a small scale.
They had production runs in the thousands. This allows some time to iron out mistakes in designs. The expectation was that early airframes would have kinks to work out. Lockheed made 195 F-22s for example, while they made 1,715 P-80s
