Until Robinson, and Branch Rickey, the players in the Negro League, no matter how good they were, did not have the option to play in the American or National League.
I think Satchel Paige (July 7, 1906 – June 8, 1982) made it to the “Bigs.”
According to a pretty good article on Wikipedia (https://en.wikipedia.org/wiki/Satchel_Paige):
“At age 42 in 1948, Paige made his major league debut for the Cleveland Indians. Paige was the first black pitcher to play in the American League and was the seventh black player to play in Major League Baseball. Also in 1948, Paige became the first player who had played in the Negro leagues to pitch in the World Series; the Indians won the Series that year. He played with the St. Louis Browns from 1951 to 1953, representing the team in the All-Star Game in 1952 and 1953. He played his last professional game on June 21, 1966, for the Peninsula Grays of the Carolina League. In 1971, Paige became the first electee of the Negro League Committee to be inducted into the National Baseball Hall of Fame.”