Jay attended Lemont High School in Lemont, Illinois. He played both baseball and football at Lemont. Jay committed to the University of Illinois to play college baseball for the Fighting Illini. As a freshman, he appeared in 18 games, going 1–3 with a 3.10 earned run average (ERA) and 20 strikeouts. As a sophomore in 2014, he took over as the closer and had 10 saves, a 1.94 ERA and 47 strikeouts. After the season, Jay played for the United States collegiate national team during the summer, and also played collegiate summer baseball for the Yarmouth-Dennis Red Sox of the Cape Cod Baseball League. As a junior in 2015, he had a 1.08 ERA, 76 strikeouts and 14 saves.
