Jack Graney was an innovator although it didn’t take hold. In 1916 he was the leadoff batter for the Cleveland Naps. He wore a miniscule number one on his sleeve. This numbering system didn’t catch on and was discontinued the next year. Oh well. That is the way of innovation some times.
Very soon though the Yankees saw a rise in popularity. A whole bunch of new fans started coming to see them play but they didn’t know who the players were by sight. So, in a bold move, they introduced numbers in 1929. They made them very big. And they put them on the back of the uniform.
The original numbering system followed the batting order so Ruth was number 3, Gehrig was 4 and so on. All teams eventually matched this by 1932. In 1952 the next “innovation” occurred with the Dodgers putting them on the front as well but never became universal.