As early as 2014, Michkov began to get noticed for his ice hockey talent, setting scoring records for his age group.

[5] He also set a new record for points by a 16-year-old in the MHL[6] In 2021, Michkov made his professional debut with SKA Saint Petersburg of the Kontinental Hockey League (KHL), with his first game coming on 2 September 2021.

[11] Michkov was considered one of the top prospects for the 2023 NHL entry draft, though some scouts and pundits speculated he may have dropped due to the ongoing Russian invasion of Ukraine.

[18] Flyers general manager Daniel Brière speculated part of the reason Michkov fell in the draft was due to his KHL contract keeping him in Russia until 2026, and expressed amazement he was able to join the team earlier than expected.

[19] Qualifying for the team out of training camp, Michkov recorded his first NHL point against the Calgary Flames on 12 October, in a 6–3 loss; he assisted on a goal by Travis Konecny.

[21] Michkov was named NHL's rookie of the month after he recorded four goals and five assists for nine points in 11 games played during October.

[22] On 30 November, against the St. Louis Blues, Michkov became the fourth teenager in NHL history to record 3 overtime goals, joining Sidney Crosby, Ilya Kovalchuk and Rick Nash as the only players to accomplish the feat.