Kochetkov first played as a youth within hometown club Dizel Penza. While with the Dizel Sports Academy, Kochetkov helped the claim the Volga region championship in 2011. With the ambition to play in the MHL, Kochetkov joined Ak Bars Kazan under-18 junior program for the 2015–16 season, however received sparse playing time, resulting in his return to Dizel Penza of the Supreme Hockey League prior to the 2016–17 season as a 17-year old. He played with junior affiliate, the Dizelist Penza of the National Junior Hockey League, before making his professional debut with Penza, playing in relief and registering 5 saves in a 6–1 victory over Yermak Angarsk on November 7, 2016. Kochetkov made 8 appearances over the course of the season, earning his first victory in his third and final start, in a 4–2 decision over Ariada Volzhsk on January 11, 2017. On July 8, 2017, Kochetkov agreed to his first KHL contract, signing a two-year deal with HC Sochi. He was assigned for the duration of the 2017–18 season to play with junior farm club, Kapitan Stupino. With Kapitan lacking in depth, Kochetkov posted just 6 wins in 31 games, while still posting a.917 save percentage. In the 2018–19 season, Kochetkov returned to the VHL, joining Sochi's affiliate HC Ryazan. He was elevated to practice with Sochi throughout the season, and made his KHL debut as a 19-year old for Sochi in a 4–2 defeat to Jokerit on October 1, 2018. He made one other appearance with Sochi throughout the season, returning to the VHL to help lead Ryazan in the post-season. On May 21, 2019, Kochetkov was traded by Sochi to contending club, SKA Saint Petersburg, in exchange for fellow goaltender Nikita Bogdanov. In the 2019–20 season, Kochetkov remained on the opening night roster and started in the opening 5 games. After an assignment to SKA-Neva in the VHL, Kochetkov returned to SKA and having collected 3 wins in 6 games was traded to his third KHL club, HC Vityaz, along with Alexei Byvaltsev in exchange for Alexander Samonov and Artyom Shevts-Rogovoi on 18 October 2019. He made his debut with Vityaz in a 4-1 defeat to Sibir Novosibirsk on 22 October 2019. In 8 games with Vityaz, as the club's third choice goaltender, Kochetkov collected 1 win while posting a.917 save percentage.
International play
Kochetkov first represented Russia at the junior level for the 2019 World Junior Championships in Vancouver, Canada. Earning the starting goaltender role, he collected 4 wins in 5 games, helping Russia claim the Bronze medal against Switzerland on January 6, 2019. As the standout goaltender of the Tournament, Kochetkov was recognized with the Best Goaltender award.
