Giaccone was born in the Ridgewood section of Queens. His father died during the 1930's, leaving Giaccone, his sisters and brothers, and mother to fend for themselves during the Great Depression. Serving as an altarboy, Giaccone grew up to be a strict Catholic. Giaccone had good grades in school and graduated from high school. As a young man, Giaccone became a protege of Bonanno underboss Giovanni Bonaventre. Giaccone was described as being brazen, yet gentlemanly; when a relative was diagnosed with hemophila, Giaccone assumed the financial support of his wife and children. Giaccone was also known to be ruthless when necessary. Giaccone was a flamboyant dresser.