Fincke was born in Pittsburgh, Pennsylvania to Edward and Alma Fincke. He graduated from the Sewickley Academy in Sewickley, Pennsylvania in 1985 and attended the Massachusetts Institute of Technology, where he graduated in 1989 with a bachelor of science in Aeronautics and Astronautics and a bachelor of science in Earth, Atmospheric and Planetary Sciences. He then attended a summer exchange program with the Moscow Aviation Institute, where he studied cosmonautics. Fincke also received a master of science in Aeronautics and Astronautics from Stanford University in 1990. He then joined the United States Air Force, where he completed pilot training in 1991 and was stationed at the Air Force Space and Missiles Systems Center in Los Angeles, California.