Already I say that they are symbolic dates. It was to put a date of when Vito turns into a boss of "gang". Because of i say 1919. In this date, according to Puzo's book, Vito kills Fanucci, acquires respect, but he does not become in a mafioso immediately. He associated with Genco in the business of the oil. Later he obtains the monopoly based on violence (it is the first time that the book mentions criminal acts on the part of Vito). But the real beginning as "gangster" is during the Prohibition, which begins in 1919. And they will call "Don" Vito, according to Puzo, with the Great Depression ( from 1930).
1933: it is also a symbolic date. According to Puzo, in the New Year's Eve of 1933 Vito kills Maranzano and begins the purge of the families, gangs, Black Hand ... until to staying with 5 or 6 families. It is established the system of 5 families in NY and "officially" born La Cosa Nostra, and the Corleone family was one of them. Also it is possible to establish the date in 1936, because, according to Puzo, to appease and to purge NY of gangs until to staying with all 5 families it was necessary 3 years. Also Puzo says that Vito raised the creation of bosses committee: the Commission.
And according to Winegardner (already I know that he is a hated man), in 1933 Vito kills Maranzano and it begins the Castellammare War, the war that purges the families and gangs and would reorganize them until to staying with 5 families. Also he says that Vito turned in capo di tutti capi.
My conclusion is that the beginning of Vito as boss of a gang would be aprox. in 1919-1920 and as "official" boss of one of all 5 families his beginning would be between 1933-1936.