Thomas Haines was born on August 9, 1933, to Elsie Cubbon Haines (1894–1955) and Charles Haines, who deserted when Haines was two. In 1937, "by reason of the insanity of the mother", a judge placed him at the Graham School, an orphanage in Hastings-on-Hudson, New York. The orphanage, now a social services and foster care agency, was founded in 1806 by Isabella Graham and Elizabeth Hamilton, the recently widowed wife of Alexander Hamilton. Haines remained at the orphanage until high school, when he became a resident houseboy and gardener for a wealthy Hastings family. The story of Haines early life appears as "From the Orphanage to the Lab" in the Story Collider podcast. and in his autobiography with Mindy Lewis, A Curious Life: From Rebel Orphan to Innovative Scientist'.
Haines attended the City College of New York, with a B.S. in chemistry in 1957 and an M.S. in education in 1959. During that time he worked as live-in baby sitter for then-blacklisted American songwriter Jay Gorney (co-writer with Yip Harburg of the Depression era anthem, “Brother, Can You Spare a Dime?”) and his wife Sondra. There Haines came to know many other blacklisted professionals including actors Zero Mostel, Paul Robeson, and Lionel Stander, philosopher Barrows Dunham, and Bella Abzug, then a young lawyer defending blacklisted artists and intellectuals at HUAC hearings.