Historically in production during April 1945 which makes it just as plausible as P-51H and F8F.
For once I agree with you. This is a hypothetical question, and if I had to base my air force around one aircraft in 1939 it would be the hypothetical 1939 Me 262. Jets were the future and I'd want to get in on the ground floor. My jets will render all your piston engine fighters redundant, just as they did in a non-hypothetical, historical sense.
Cheers
Steve