Well, there you go. US bias hits again. It took decades to get from the concept to a working suborbital rocket but about decade to go from that to the moon. Konstantin Tsiolkovsky had the concept in Tsarist Russia but it took advances in Nazi Germany (V-2) and Soviet Union (R-7) to put someone into space. Konstantin Tsiolkovsky already had the concepts for a) chemical rockets b) propellants, namely liquid oxygen and liquid hydrogen c) multiple rocket staging to escape Earth's gravity. he even computed the mass ratios for staging at 10:1.
But you are correct that iteration can be damned hard. The F-1 engine used in the Saturn V moon rocket is one example. It had a single large chamber which was much cheaper to manufacture and more reliable. Soviet rockets either used multiple-chambers or used many smaller engines. Even the RD-170 is like that. You know why? Because of something called combustion instability. The Soviets never managed to solve it properly until really late in the game if ever. Destructive resonance in those combustion regimes caused vibrations which led to the explosion of the engine into tiny pieces. But they did come up with tricks the US didn't. Like channel wall nozzle design which is now a de facto standard in not only Russian but also US and Chinese rocket engines.