You have an unduly rosy picture of rocket science. The turbopump used in most liqued fueled rockets to presurize the fuel is notoriously complicated. Small changes to the design can result in a dramatic loss of efficiency, or even worse if it starts cavitating the pump can eat itself. For this reason nearly nobody designs turbopumps from scratch and first principles, they take a well understood design and maybe tweek it a bit. And you can bet that they then test those tweeks on a bench a lot.
Similarly devilishly complicated is the injector design. Obviously you want to mix the oxidizer and fuel in the optimal ratio for the highest efficiency. That’s the easy part. But then you also want to offset from this optimum near the edges to produce a colder flow near the nozzle wall to protect it from melting. Of course nowadays people do a lot of computer simulations to save on testing time, but it is still not uncommon to discover combustion instabilities or hot-spots in the engine tests.
So no, nobody can, let alone did, design a rocket entirely in a computer and then send it to the moon without many many tests, and incrementally improved tribal knowledge.