Olimb was a star player in high school, helping Warroad High School reach the state tournament twice. Because he turned 18 before the start of his senior season, Olimb was eligible for the 1987 NHL Entry Draft and became one of the few high school players to have already been drafted after the Minnesota North Stars selected him in the 10th round. He continued to show his talent that season and received the Mr. Hockey Award as the top player in the state. He would later be ranked as the 33rd best player in the history of Minnesota High School Hockey.
