Jost chose the collegiate route to help create a path to the NHL. Though Jost was selected by Everett with the No. 7 pick of the 2013 WHL Bantam Draft, he turned down a career in major junior hockey to play with Okanagan of British Columbia Major Midget League to retain his NCAA eligibility. He had 88 points (44 goals, 44 assists) in 36 games as Okanagan's alternate captain in 2013-14 to help it win the BCMML championship.
Before 2015-16, his second full season with Penticton of the British Columbia Hockey League, Jost committed to the University of North Dakota for 2016-17. He was selected by the Colorado Avalanche with the No. 10 pick of the 2016 NHL Draft.