*Club domestic league appearances and goals, correct as of 02:35, 9 January 2023 (UTC) ‡ National team caps and goals, correct as of 08:30, 13 July 2020 (UTC)
Baumann began his career in Switzerland with the youth teams of Urdorf and Oetwil-Geroldswil. In 2006, he joined the youth team of FC Zürich.
Zürich U21
In December 2012, Baumann was promoted to the U21 team of FC Zürich.
Loan to Höngg
In 2013, Baumann was sent out on loan to SV Höngg. He made his debut for the club in a 2-1 win against FC Thalwil.
After his 3-month loan spell, he returned to Zürich. He made a total of 2 appearances for the club.
Loan to Wil
In 2015, Baumann joined Swiss Challenge League club Wil in a 3-month loan deal.[1] Baumann then returned to Zürich. He made 1 appearance for the U20 team.
Zürich seniors
In July 2015, Baumann was promoted to the senior team of Zürich. In 2016 he made his league debut for the club in a 0-2 defeat against his former club Wil.
Loan to Rapperswil-Jona
Baumann was sent on loan to Swiss Challenge League club Rapperswil-Jona.[2] He made his debut for the club in a 2-0 away defeat against Wil.[3] After his loan spell, he returned to Zürich, making a total of 4 appearances for Rapperswil-Jona.
Return to the senior team
Baumann was demoted to the U21 team in February 2019.[4] After playing mostly for the U21 team, Baumann was once again promoted to the senior team replacing outgoing goalkeeper, Osman Hadžikić.[5][6]