But I'm wondering how Carlo Gambino's family could have surpassed the Genovese family at some point, without initiating new members from 1957 till 1972. How could they have got 300 made men back then?

Multiple sources (including the Mafia Encyclopedia, Mafia dynasty, and even Jeri Capeci if I remember correctly) state that Carlo Gambino made his family one of the most if not the most powerful during his reign. John H. Davis, the writer of Mafia Dynasty, even writes that it's just a myth that the mob didn't initiate new members from 1957.

Another example is Joe Massino, who reputedly made his Bonanno family almost rivaling the Gambinos in numbers of made men, when they were previously decimated during the 1980s trials.