Hülsmann joined the youth academy of German club Bayern Munich at the age of twelve from Eintracht Trier.[3] On the beginning of the 2023–24 season, he was called up for the Bayern Munich senior team as the backup goalkeeper to Sven Ulreich, after the team transferred Yann Sommer and the starting goalkeeper Manuel Neuer was still recovering from an injury, Hülsmann also established himself as the first option for the reserve team Bayern Munich II.[4] He featured on the bench for the 2023 DFL-Supercup match on 12 August 2023 against RB Leipzig that ended 0–3 as a defeat.[5] He also started the Bundesliga season as the second goalkeeper.
On 23 August 2023, Hülsmann signed a professional contract with Bayern Munich until 30 June 2026.[6]
Hülsmann is a native of Trier, Germany.[10] He has regarded Germany international Manuel Neuer as his football idol.[11] His younger brother Gregory Randy Hülsmann plays for the under-17 side of 1. FC Kaiserslautern as a goalkeeper as well.