Raum was born in Nuremberg and started playing football at the local club Tuspo Nürnberg at the age of four. At the age of eight, he was scouted to the youth academy of SpVgg Greuther Fürth in the neighbouring town and progressed through their youth teams.[3]
As an under-19 footballer, Raum gained his first experience in the senior sides and was part of the first team from the 2017–18 2. Bundesliga season. In the first two rounds of the 2017–18 DFB-Pokal he scored in both games,[4] but did not make it to the final round with his team after a defeat against FC Ingolstadt. He also made 20 appearances in at second-highest German level and mainly played as a substitute in the following seasons. His contract, which was set to expire in June 2020,[5] was extended with an option for an additional year in May 2020.[6]
Hoffenheim
After the 2020–21 season, in which Greuther Fürth won promotion to the Bundesliga, Raum moved to TSG Hoffenheim as a free agent, having signed a pre-contract with the club in January 2021. He signed a four-year contract with Die Kraichgauer.[7] On 11 December 2021, he scored his first Bundesliga goal in a 2–1 away win over Freiburg.[8]