Jay and his family live in Hanover, New Hampshire.He grew up in a middle-class neighborhood in Levittown, NY. His father, like most of the fathers in the neighborhood, was a veteran of World War II, having served as an Army paratrooper throughout the war, and his mother was a homemaker. Jay attended local public schools, and in 1969, during the summer before he started high school, he watched with millions of other Americans as Neil Armstrong took the first steps on the moon.

With the help of his parents, student loans, scholarships, summer jobs, and jobs in the dining halls during the school year, Jay attended Cornell University. He earned a B.S. in electrical engineering in 1977, and later graduated with an M.D. from Cornell Medical School in 1981. After his internship, he worked as a physician specializing in space research. Jay was on the faculty of the University of Texas-Southwestern Medical Center from 1984-1995 where he did biomedical space research and served as the medical director for the walk-in clinic at Parkland Memorial Hospital. He also served as a Major in the U.S. Air Force Reserve from 1987-1995. As a flight surgeon with the 457th Tactical Fighter Squadron in Fort Worth, TX, he flew in the back seat of the F-4 and F-16 aircraft.