He didn't want to be another downtrodden immigrant, a slave of the dominant Anglo-Saxon white ruling class.

Having said that, from the account of Vito's rise to power given in the novel, it seems that he stumbled into the role of Mafia Don almost by accident - by the chance meeting with Clemenza, the incident with Fanucci and the decision to kill him rather than to pay him tribute. Then, Fanucci's old associates began to pay Vito without Vito having to do very much. From then on it was a snowball effect - he accumulated more "favours" and his reputation spread.