Black players had been in the NFL since 1946 when the Rams signed Kenny Washington and Woody Strode. The AAFC was actually first with the Browns signing Marion Motley and Bill Willis prior to the Rams signing their guys.
By the time the Cowboys were even considered as an expansion team every team in the league had several black players except the Commanders of course.
Marshall was instrumental in getting black players unofficially banned when he started the Boston Braves in 1932. Prior to that there had been a number of black players in the NFL including one black HC, Fritz Pollard. Actor/singer Paul Robeson, best known for his role in the musical "Show Boat" played in the NFL in the early 20s.
Marshall was influential among the owners because he brought a great deal of financial backing into the league at a time when many teams were struggling. In return for loans the owners pretty much gave in to whatever he wanted to do. He was a staunch racist and didn't think it was right for whites and blacks to "mix" so he pushed for them to be quietly blocked from playing in the NFL.
Once the Browns signed black players the Rams were quick to follow and within a few years nearly every team was drafting black players.
To be a little bit fair, not a lot of black athletes were in college back then so there was not nearly the number to choose from in the draft as there is now. Scholarships were not awarded as easily and most colleges were not integrated yet so the small numbers of black players in the 50s should not be construed as the NFL keeping them out. Once the gate was open teams were quick to sign quality players. There just wasn't that many available at the time.
Once the 60s and Civil Rights came along the number of black football players in college increased dramatically and the draft reflected that as well. The AFL in particular drafted a lot of black athletes and the NFL didn't want to be left behind. Scouting at black colleges like Grambling had been nearly non-existent, until the AFL came along. Plus there was still a lot of southern players & coaches who didn't want black players on their teams. It took time to break that bias down but eventually it happened.
Sorry for the history lesson this morning...