West graduated from East Bank High School in 1956, and more than 60 universities showed interest in him. He eventually chose to stay in his home state and attend West Virginia University (WVU), located in Morgantown. In his freshman year (1956–57), West was a member of the WVU freshman squad that achieved a perfect record of 17 wins without a loss over the course of the season; other team members included Jay Jacobs and Willie Akers. In his first varsity year under head coach Fred Schaus, West scored 17.8 points per game and averaged 11.1 rebounds; he also started in all 28 games while shooting 49.6% from the field and 73.2% from the free throw line. These performances earned him a multitude of honors, among them an All-American Third Team call-up; First Team All-Southern Conference; Southern Conference Tournament Most Valuable Player Award and First Team honors; Chuck Taylor–Converse Second-team All-American honors; and Associated Press and United Press International Third-team All-American honors. The Mountaineers went 26–2 that year, ending the season with a loss to Manhattan College in post-season tournament play.