There's no "magical" answer here — they started to realize that this was going to be an issue, they started asking the major production companies to develop prototypes, they poured a lot of money into it. Just prior to the war started to mobilize practically every US scientist for work on one war project or another. They also collaborated and exchanged technical information with some other allied countries (primarily the UK). They developed an elaborate technical talent draft system for identifying people who would be useful for these kinds of projects and made sure they worked on them, rather than being sent to the front. They took the manufacturing industry that they had already spent decades developing (e.g. Detroit) and converted it to war production. They managed to coordinate work between the military patrons, industrial contractors, and university scientists in a way that was extremely productive... and very expensive. (The development of the B-29 Superfortress, as is fairly well known, cost more than the Manhattan Project.)

But I would take issue with the idea that they "perfected" this technology. They got it to work. It was hardly "perfected." As the early Cold War demonstrated, they still could do a lot to improve carriers, bombers, escorts, and so forth. And there were some who thought that the system described above could even have been better (e.g. there were many who thought that Vannevar Bush's OSRD contract system was inhibiting development by tying too much of it to Bush's own opinions about what was a good idea and what wasn't).

The fact that the USA suffered zero homeland attacks meant that it was pretty unfettered to research and produce whatever it wanted. Germany and Japan continued to roll out new, pretty impressive tech during the war but under intense bombing their production pipeline and access to raw materials like fuel got seriously disrupted. The physical isolation of the USA, combined with its preexisting massive industrial base, huge labor pool, and strong scientific system, somewhat uniquely positioned it to really exploit new developments in technology during the war.

The United States also was a much smaller power militarily speaking just before world war II, so a lot of the military buildup occured after newer weapons were developed as oppsed to lets say Germany who began their buildup in the 20s. In fact before the war the US ranked 17th in the world behind Romania source

So for instance, the US began the war with its most commonly issued rifle being the M1903 Springfield, a boltaction rifle which was a contemporary of the german K98 and the British Enfield (all saw service during WWI)

But within a year or so America had produced enough M1 Garand rifles (which were semi-automatic) to eclipse the older models bringing that particular category into a sort of next gen phase, as opposed to Germany and the UK who had simply been at war much longer and had to prepare for war much earlier.