Welch attended high school in Dansville, New York, where he played football at the halfback and linebacker positions.
After missing most of his sophomore year with an ankle injury, Welch gained 467 yards on 117 carries as a junior in 1971.
[3] Welch graduated from Ithaca in 1973 and worked from 1973 to 1976 as an assistant football coach at Rush–Henrietta Senior High School in Rochester, New York.
Welch accepted the offensive coordinator position at Washington University in St. Louis in 1980 and remained there for four years.
"[2] Welch spent ten years as an assistant coach at Ithaca, and during that time, the football team won national championships in 1988 and 1991, made NCAA playoff appearances in 1985, 1986, 1990, and 1992, and participated in the Eastern College Athletic Conference ("ECAC") playoffs in 1984 and 1987.