Born in Policoro in the Province of Matera, Zaza grew up in Metaponto and began his youth career with Stella Azzurra from Bernalda in 1997. He remained with the organization until 2002, when he moved to the youth academy of Valdera at the age of 11. He remained until 2006, when he was scouted by Serie A side Atalanta, whom he joined shortly after. He remained within the club's youth team for four years and even began to earn senior call-ups towards the end of the 2008–09 Serie A campaign. He made his Serie A debut on 1 March 2009 in a 0–2 home defeat to Chievo Verona as an 86th-minute substitute for Ferreira Pinto. He made two further substitute appearances for Atalanta that season, though he remained within the club's youth setup for the entire 2009–10 Serie A campaign.