Levy grew up in Salt Lake City and played high school hockey in the region. He took a chance to advance his career by moving to Minnesota for his senior year. He managed to get on the Rochester Mustangs as a third goaltender and played well in his minimal appearances. The following year he became the team's starter and began to make a name for himself. Levy helped the Mustangs win the US National junior ice hockey championship in 1990 and he used the notoriety to earn a scholarship to the University of New Hampshire. Levy was also selected by the Minnesota North Stars in the NHL Draft that summer, something he admittedly didn't fully comprehend.