Williams was born in Plainfield, New Jersey, the son of Isabel Lamson and Harrison Arlington Williams, and graduated from Oberlin College in 1941. He engaged in newspaper work in Washington, D.C., and studied at the Edmund A. Walsh School of Foreign Service of Georgetown University until called to active duty as a seaman in the United States Naval Reserve in 1941. He became a naval aviator and was discharged as a lieutenant, junior grade, in 1945. After being employed in the steel industry for a short time, he graduated from Columbia Law School in 1948, and was admitted to the bar and commenced practice in New Hampshire. He returned to Plainfield in 1949 and continued to practice law, and was an unsuccessful candidate for the New Jersey General Assembly in 1951 and for city councilman in 1952.
