Judge Green was born on April 2, 1923 in Philadelphia, Pennsylvania. His father, Robert Lewis Green, had come to the United States from St. Thomas island in the U.S. Virgin Islands. Green attended West Philadelphia High School, graduating in 1941. He initially had "no thought of going to college," intending instead to go immediately to work. From 1941 to 1942 he worked in a Philadelphia restaurant and at a drug manufacturing company. In 1942 he took a job with the United States Army Signal Corps.