After playing for Ilves in his youth, Leinonen moved to JYP's Under-16 program.[4] He played for the JYP Under-16 team in 2018-19, and the Under-18 team in 2019-20. After playing 15 for the Under-20 team in 2020-21, Leinonen played 21 games for the Under-20 team in the 2021-22 season and played 4 games in Liiga for the senior team.[5]
Going into the 2022 NHL Entry Draft, Leinonen was regarded as the top goaltending prospect[6] and was ranked as the top European goalie by NHL Central Scouting.[7] He was drafted 41st overall by the Buffalo Sabres, as the first goaltender selected in the 2022 NHL Entry Draft.[3] He attended Buffalo Sabres Development Camp in 2022, 2023, and 2024.[8][9]