Mangano attended Manual Training High School, New York Prep, and St. John's College. He was a member of Phi Sigma Chi and the Colleague's Club. He initially went to work in his father's funeral home. In 1934, he was elected to the New York State Assembly as a Democrat, representing the Kings County 8th District. He served in the Assembly in 1935, 1936, and 1937. He was an alternate delegate in the 1936 Democratic National Convention, and would serve as a delegate for the 1940, 1956, 1960, and 1964 Democratic National Conventions. In 1937, he was elected Sheriff of Kings County. He served as Sheriff from 1938 to 1941. In 1941, he was elected a member of the New York State Democratic Committee. In 1942, the position of Sheriff of Kings County was abolished and replaced with a single, city-wide sheriff, making him the last Sheriff of Kings County.