Before becoming part of the Corleone family, Luca Brasi could have been a survivor of some sort of local gang warfare in Sicily. He may have lost his home or loved ones in the chaos. This experience made him tough and fearless. He was looking for a purpose and a place to belong, and the Corleone family provided that. His skills in combat and his lack of fear made him an ideal candidate for the family's enforcer role.
Luca Brasi might have been a loner or an outcast in his pre - Corleone days. He could have been a man who had few friends and was just trying to get by. Maybe he worked odd jobs here and there, but his violent tendencies always made him stand out. And that's what caught the attention of the Corleone family.