1. FC Köln

In his youth years, Thielmann first played in the then youth game community Hetzerath / Föhren / Bekond and switched to the youth team of Eintracht Trier for the 2014–15 season. For the 2017–18 season, he moved to the U17s of 1. FC Köln.^[3] He played 24 games for the team and won the championship with them in June 2019 after a 3–2 win over Borussia Dortmund.

In the 2019–20 season, Thielmann was promoted to the U19s. He made his professional debut with 1. FC Köln in a 2–0 Bundesliga win over Bayer 04 Leverkusen on 14 December 2019.^[4] In doing so, he became the first footballer born in 2002 to play in the Bundesliga, and was the second youngest league debutant for his club after Yann Aurel Bisseck.^[5]

After a convincing debut, manager Markus Gisdol continued to start Thielmann in games against Eintracht Frankfurt and Werder Bremen.^[6] In January 2020, Thielmann signed his first professional contract. The collaboration between him and 1. FC Köln was extended until 30 June 2022.^[6] "He is very, very advanced for his age, both physically and physically, and he also has a very good understanding of the game. We trust him that he will hold his ground in the long term," said sporting director Horst Heldt in justification go the contract extension.^[6]

On 5 December 2020, Thielmann scored his first goal as a professional in a 2–2 draw against VfL Wolfsburg.^[7] On 20 January 2021, he scored an injury time winner against Schalke 04 in a relegation six-pointer. On 30 April 2021, the club announced that Thielmann's contract had been extended until 2024.^[8] In June 2022, he was nominated for the Golden Boy, an award given to the best under-21 player in European football.^[9]