Greenspan attended James I. O'Neill High School in West Point, New York where his father was Athletic Director for the United States Military Academy.
Before the 2015 season, Greenspan joined the Arizona State Sun Devils baseball team as an assistant coach.
[7] Greenspan then joined the Cal Poly Mustangs baseball team as an assistant coach in 2022, spending one year there.
[8] After his sole year at Cal Poly, Greenspan became an associate head coach again, now joining the Michigan Wolverines baseball team for the 2023 season.
[9][10] Following one year at Michigan, Greenspan was hired as the head coach on August 18, 2023, for the Northwestern Wildcats baseball team before the 2024 season.