[The Game]

If you have minors checked and the new players come in after the season is over then Gehrig coming in the offseason of 1920 is accurate since he was in Single A in 1921.
Gehrig attended PS 132 in the Washington Heights section of Manhattan, then went to Commerce High School, graduating in 1921.[24][25] He then studied at Columbia University for two years, before leaving to pursue a career in professional baseball.[26] Initially, he went to Columbia on a football scholarship, where he was preparing to pursue a degree in engineering. Before his first semester began, New York Giants manager John McGraw advised him to play summer professional baseball under an assumed name, Henry Lewis, despite the fact that it could jeopardize his collegiate sports eligibility. After he played a dozen games for the Hartford Senators in the Eastern League, he was discovered and banned from collegiate sports his freshman year.[27] In 1922, Gehrig returned to collegiate sports as a fullback for the Columbia Lions football program. Later, in 1923, he played first base and pitched for the Columbia baseball team.[27] At Columbia, he was a member of Phi Delta Theta fraternity.[2
https://www.baseball-reference.com/r...d=gehrig001hen