Heading into the 2017 NHL Draft, Swayman played for the Sioux Falls Stampede of the USHL. In his draft season, Swayman posted a record of 7-18-3, a rather unimpressive total, but during that year he also secured a save percentage of .914 and a 2.90 goals against average. Both extremely impressive numbers on a losing team.
Heading into the draft, Swayman confirmed that he hadn't received much interest, but one team in specific maintained constant contact. That team was the Toronto Maple Leafs. As day 2 of the draft continued on, the Leafs owned pick #110. When that pick arrived and Swayman was still available, he thought his name might be called. The Buds, instead, opted for Prince Albert Raiders goaltender Ian Scott.