Moore was born in the Oak Square section of Brighton, Massachusetts in Boston on May 18, 1914, the son of Frederick T. Moore Sr. and Susan Frances (O'Donnell) Moore. He was the second oldest of six children. His father was a regional sales representative for Dunlop tires and worked hard to earn a modest income. Moore came from a family whose roots in the United States go back to the 1630s and include ancestors who fought in the American Revolution at the Battles of Lexington and Concord, the Battle of Bunker Hill and the American Civil War.