Tocco was a second generation Italian-American, whose grandparents were from Italy. He was the youngest of his siblings, and grew up in south suburban Chicago Heights, Illinois. Tocco had two sisters, Anne (Goff) and Marie (Mattio) and a brother, Joe Tocco. Albert Tocco's father, Michael Tocco, was a decorated World War I veteran and an accomplished business man. During the Great Depression, six-year-old Tocco was already working to help support his family. Once a teenager, he helped his father run the largest cement business in Chicago. Tocco was 17 when his father died from cancer.