Šćrbec went through the youth ranks of NK Dinamo Zagreb until he moved with his brother Lovro to the youth team of NK Zagreb in 2006, playing several games for the Croatian U-16 national team in 2007. He was a part of the U-17 national team in 2008 but remained uncapped at that level. He returned to his former club in his last year as a junior team player, 2009, only to be sent to NK Lokomotiva Zagreb in January 2010, signing a stipend contract initially and then a 7-year professional contract in August 2010. Lokomotiva proceeded to send him on a season-long loan to the Druga HNL team NK Rudeš. In July 2011 his contract was mutually terminated and he moved to NK Inter Zaprešić.
