Made by whom? Did he make himself? The thing is, he could only have been made by another Don in New York, and then would have subsequently become part of that family.

I think it's the most plausible that he was made back in Sicily by his cronies in Corleone. He went to Sicily just a few years after he killed Fanucci. The novel also describes that he started to formally organize his family, making Clemenza and Tessio capos and Genco consigliere, somewhere in the 1920s. I think this happened when he returned from Sicily, after being formally inducted as a man of honor and being able to induct others into the Mafia.