A BB I n real life takes 4 years or so to complete after being "laid down". While you can't start all the ships on time you can get them all done before 1944. I generally end up with 35-40 NIC total if going for a historic navy. But let's face it you don't need a historic navy to defeat Italy and Germany. And if you blob your navy you can defeat Japan without US help.
As far as I can see it, there is no way known you can get ENGs historic naval production (and I'm just counting HoI4 ships, so DEs, CVLs, CVEs, sloops, corvettes, landing ships, MTBs and anything else I've forgotten are off the table) with 35-40 IC before 1944 - I built up to over 80 IC, and wasn't close by 1945, and I was carefully taking account of every ship, and didn't build any surplus anything (and build a good deal less merchant marine than was historic, because convoy raiding isn't near as lethal as it should be, particularly if the AI is doing it). If you'd like me to get a list of ships that need to be built to achieve it, I'm happy to provide, but you won't hit it with 35-40 NIC unless you're playing a mod that does some pretty crazy things to shipbuilding, or hitting the console cheats. I'm not trying to be harsh here, I'm sure you thought you came close to ENG's historic naval production, but when you crunch the numbers on ships actually built, that's just not enough NIC.
For example, remember that you need 39 NIC to have one factory on each ship laid down in 1937 alone, and one NIC on a CV or BB won't get it done in four years - more like 10-15. Your CLs will be falling behind as well (and ENG built more CLs in per ship terms than USA during this period, and one NIC won't get you a CL in the 2-3 years they take to build - nowhere near), and once you get to 1938/39, ENG starts going pretty crazy laying down destroyers and builds quite a few submarines as well.
I do agree that if you do this, you're well and truly overdoing it (particularly with vanilla naval settings, but even with some nips and tucks that makes it a little harder to wail on the AI), but the question was one of whether the production could be achieved, not whether achieving that production was sensible in the current in-game context.
Happy to be proven wrong here of course

, but I wouldn't mind seeing some screenshots of actually built navies rather than just assertions.