Sorry, menyak. Nice try, but no cigar... First of all, the All-American Girls' Professional Baseball League was founded in 1943 (as the All-American Girls' Softball League, by the way). But there were literally hundreds of teams before that league was founded, and the earliest played its first game quite a bit earlier... Any guesses? I'll give this to anyone within five years.
Good movie, by the way, and historically pretty accurate, with a few minor exceptions.