This is close but not quite right.
In Early 1939 the USN was putting out the requirement for the SB2C. It took quite a while to get that thing to even be half way right.
March of 1939 was when they issued the requirement that lead to the Avenger. They got 13 proposals and by late summer had whittled the field down considerably. By Nov 1939 it was down to two prototypes from Grumman and one form Vought although contracts wouldn't be signed for another 6 months.
The Navy had ordered the XF4U in June of 1938, inspected a mock up in Feb of 1939 and had a flying prototype in May of 1940. Yes it needed hundreds of changes.
Grumman had done a couple of designs in 1938 for fighters to use the Wright R-2600 engine but put them aside to work on the F4F and the TBF, Grumman started work again in Sept 1940, because as you say, the war in Europe was showing that better aircraft than the F4F were going to be needed in the near future.
This is leaving out some of the other prototypes and also rans. The Force structure was tweaked and the aircraft capacities were adjusted bit but the USN fought the war in 1943/44 with the aircraft they had planned in 1938-40.
They had several advantages, The R-2600 was in small scale production in 1939 with 163 made and with 1925 built in 1940 the Navy was somewhat assured they had a decent powerplant for the intended aircraft. The R-2800 was flying in XF4U-1 in the summer of 1940 with an 1800hp engine (it went through several).
The USN was not learning much from the RN. Perhaps they should have so their torpedoes wouldn't be so bad?
Now the US was not trying to fight the war at the same time so development of prototypes went a bit faster than in Britain. The TBF went fast, the SB2C which started earlier finished later, good thing we had the SBD
The USAAC maybe could have used some more/better lessons. But the order for the P-47 was placed in 1940 and the P-43 orders were only intended to help fund factory expansion and to keep the work force together and enlarge it and train it so it would be ready to make the P-47s when the time came.
A-20, B-25, B-26 and B-24 were all prewar designs although a lot tweaking to the armament (adding power turrets) went on.