Omić started his career with SV Ried in 2011, staying at the club until January 2017, when he joined Red Bull Salzburg's academy, aged 13.

[2] In the 2021–22 season, he made 33 appearances for the Italian side,[3] and helped them reach the UEFA Youth League semifinals, their best-ever placement in the competition.

[4] On 16 March 2022, Omić made his professional debut with Juventus U23 — the reserve team of the Italian club — , coming on as a substitute in the 87th minute of a 2–1 defeat against Lecco.

[5] On 18 June 2022, Omić joined the Austrian club Wolfsberger AC on a permanent deal, signing a three-year contract.

[7] He subsequently made his Bundesliga debut on 28 August, as he played the entire league match against WSG Tirol, which ended in a 1-3 win for his side.