Selected by the Avalanche in the third round (63rd overall) of the 2019 NHL Draft, Stienburg recorded 46 points (20g/26a) in 73 career NCAA games at Cornell University. He appeared in 18 games as a senior in 2022-23 (2g/5a), missing 16 contests due to an injury sustained in late December. Following his college season, Stienburg, 22, joined the Colorado Eagles (AHL) where he recorded one assist in four regular-season games and also one helper in four Calder Cup Playoff contests.
As a junior in 2021-22, Stienburg was named to All-ECAC Hockey Second Team after leading Cornell with 29 points (13g/16a) in 28 games. During his freshman season in 2019-20, Stienburg registered 10 points (5g/5a) in 27 games and ranked first among all ECAC rookie forwards with a +12 rating. He did not play during the 2020-21 campaign due to the cancellation of the Ivy League season.
Prior to joining Cornell, Stienburg played for St. Andrew's College in Ontario from 2017-19, collecting 128 points (60g/68a) in 93 CAHS league games and producing 32 points (11g/21a) in 20 CISAA (Conference of Independent Schools Athletic Association) outings. The Halifax, Nova Scotia, native also recorded 10 points (5g/5a) in eight total postseason contests to help St. Andrew's win the league championship two years in a row. Stienburg served as team captain his second season in 2018-19. The 6-foot-1, 182-pound center joined the Sioux City Musketeers of the USHL following the conclusion of that campaign and registered one point (0g/1a) in three games.
Matthew's father, Trevor, played nine years of professional hockey, including 71 games with the NHL's Québec Nordiques.