Malinin began skating in 2010 under the tutelage of his parents, who were both Olympic skaters for Uzbekistan. He is the 2016 U.S. national juvenile champion, the 2017 U.S. national intermediate champion, and the 2019 U.S. national novice bronze medalist; he did not qualify for the 2018 U.S. Championships. Internationally on the advanced novice level, Malinin is the 2018 Asian Open Trophy champion and the 2018 Golden Bear silver medalist.