"Jet Propulsion" - in a timeline from early 1942 to 1946/47
Lockheed proposed a jet design but got denied (L1000/L-133), Bell got the first contracts, (P-59) but failed in a design that would exploit the technology, Lockheed came back and produced a successful product (P-80), Republic upped the ante, (F-84), McDonnel and Grumman Navalized the technology, (F9F, F2H), North American refined it (F-86).
And when you say "got" jet propulsion the earliest? By that I mean, went "all-in" (or close to it) on jet designs" understand that manufacturers very rarely go out on their own to develop new technology unless they are going to be paid for development. Lockheed submitted a proposal in early 1942 but was rejected. When they got the go-ahead with the P/F-80, I think it's evident they "went all in," but then again they had a secured contract.