Šošić started his professional career at Hajduk Split, playing first in its reserve team, before being loaned to Zrinjski Mostar in 2021 and to Radomlje in 2022.
Šošić started playing football at his hometown club Iskra Bugojno in 2007, before joining the youth academy of Željezničar in 2011.
[1] He made his professional debut playing for Hajduk Split's reserve squad against Opatija on 14 August at the age of 18.
[3] In September, he suffered a severe knee injury, which was diagnosed as an anterior cruciate ligament tear and was ruled out for at least six months.
[7] On 9 January 2025, Šošić joined Željezničar on a free transfer, signing a two-and-a-half-year contract.