Bae began his professional career with Daejeon Hana Citizen, helping them gain promotion to K League 1 in the 2022 season.

After impressing in his debut season in the Korean top flight and for the South Korea U20 team he moved to European football with English Championship club Stoke City in August 2023.

[3] He made eleven appearances in his first season with Daejeon as he helped his team win the promotion play-offs against Gimcheon Sangmu.

[5] On 27 August 2023, Daejeon officially announced that they had reached an agreement with EFL Championship side Stoke City for the transfer of Bae on a permanent deal.

[14] After representing South Korea at under-19 level in a number of friendlies, Bae was called up to the under-20 squad for the 2023 AFC U-20 Asian Cup qualification.

[3] Bae has cited fellow South Korean Hwang In-beom, as well as Kevin De Bruyne, as his biggest footballing role-models.