Before USL: Čuić joined Dinamo Zagreb’s youth academy in 2015 and rose through the ranks from the club’s Under-15 squad to the reserve team by the start of 2018. Čuić made his debut in the 2. HNL – the Croatian second division – with Dinamo Zagreb II in April of 2018, making two appearances in the latter stages of the club’s 2017-18 campaign. Čuić became a regular in the Dinamo Zagreb II lineup in the second half of the 2018-19 season, making 15 appearances before playing in a further 14 games in the opening period of the 2019-20 season – tallying his first league goal against Medjimurje on Sept. 21, 2019.
Earlier in the year, Čuić helped Dinamo Zagreb’s U-23 side advance to the Premier League International Cup final by beating Southampton 3-1 in the semifinal, with Čuić coming off the bench to tally the final goal of the game. During the club’s Under-19 UEFA Youth League appearance in 2016, Čuić started in one game, helping his side claim a 1-0 victory on the road against Italian giants Juventus on Dec. 7, 2016.
International: Čuić has represented Croatia’s Under-16 and Under-19 National Teams, making his debut for the U-19s in a friendly against Italy on Nov. 8, 2016.