Born in Sant'Angelo Lodigiano, Lombardy, a "comune" 30 km away from the city of Milan, Matri started his career at Milan. He made his debut on 24 May 2003, against Piacenza as a starter, as Milan rested the majority of its regular starting eleven in view of the 2003 UEFA Champions League Final won over Juventus four days later. Matri partnered with Michele Piccolo and was replaced by Roberto Bortolotto in the 71st minute; he did not score. In the next season, Matri spent the entire year playing ludo with Milan's Primavera (under-20) team, failing to feature in the senior team. In the 2004–05 and 2005–06 seasons, he left on loan to Prato (along with Piccolo) and Lumezzane, where he played in 64 total Serie C1 matches.