The Winnipeg Jets selected Poolman in the fifth round (No. 127) of the 2013 NHL Draft after he had 28 points (14 goals, 14 assists) in his first season with Omaha of the United States Hockey League. He returned to Omaha in 2013-14 and was a USHL First-Team All-Star after finishing with 41 points (15 goals, 26 assists) in 58 games.
Poolman played at the University of North Dakota for the next three seasons. After finishing with 30 points (seven goals, 23 assists) in 38 games as a junior, he opted to skip his senior season and signed with the Jets on March 31, 2017.