Most crime historians who have researched this topic agree that the Genovese family started with Joe Masseria in the early 1920s. He was successful in linking to him elements from the Neapolitan and Calabrese gangs.
Different sections of New York had different ethnic compilations. Not only between the Irish, Jews, Poles, etc., but also between different Italian immigrants. I´m sure that a native New Yorker, who´s a member of this forum, can explain this better than me.
Bonanno family was originally composed of immigrants who originated from Castellammare del Golfo, and who had settled mainly in the Williamsburg section of Brooklyn, but also in Manhattan's Lower East Side. There are hints that this family was active already at the beginning of the century. That is already around 1900-1905. The leaders had simply transferred their traditions across the Atlantic, with the immigration.
Tata D'Aquila led a third family already around 1910. This family was mainly composed of men from the Palermo area, and later became the Gambino family. D'Aquila was the capo di tutti capi until he was killed in 1928.
It seems that Profaci formed his Mafia family in Brooklyn sometime in the mid 1920's. It seems that he had his top position in the Mafia confirmed during the Cleveland meeting that got broken up by the police in 1928. But who really knows?
Another interesting thing with the Profaci family is that it was largely composed of men from the small coastal town of Villabate, just east of Palermo.
The fifth family had its own territory in the Bronx and East Harlem. It was led by Gaetano "Tommy" Reina who was murdered in 1930.
It is not possible with certainty to determine how this family was formed, although there are some suggestions saying that it was an off shoot from the Morello gang. No one can tell for sure. This family was mainly composed of men from the brutal Sicilian town of Corleone.
There were members from Palermo in all these families.
If we ignore the Masseria gang, mainland Italians began to become members of the Mafia later in the 1930s, although there were exceptions. For example, Albert Anastasia (who was Calabrese, had a leading position in the Mafia already around 1930)