In January 2019, Baumgartner was promoted to the first team squad ofTSG Hoffenheim.[5] He made his debut for Hoffenheim in theBundesliga on 11 May 2019, coming on as a half-time substitute forNadiem Amiri in the 0–1 home loss againstWerder Bremen.[6]
In August 2020, Baumgartner was called up for theAustrian senior team for the first time.[17] On 4 September, he started his first match in a 2–1 away win overNorway during theUEFA Nations League.[18] Three days later, he scored his first goal in a 3–2 home defeat againstRomania.[19]
On 24 May 2021, he was named in Austrian squad for theUEFA Euro 2020.[20] On 21 June, he scored the only goal for Austria in a 1–0 win overUkraine, to help his national team to reach the knockout stages of the competition for the first time in their history.[21]
On 23 March 2024, Baumgartner scored what is believed to be the fastest goal in the history of international football, scoring after only six seconds in a 2–0 friendly victory overSlovakia inBratislava.[22] Later that year, on 7 June, he was named in the 26-man squad for theUEFA Euro 2024.[23] On 21 June, he scored his country's second goal in a 3–1 victory overPoland during the group stage.[24]