Cossette grew up in Saint-Hyacinthe, Quebec, and played for numerous amateur and youth teams between 2002 and 2007, including Inter Street-Hyacinthe, Cosmos Granby American Automobile Association, Football Club Select Rive-Sud American Automobile Association and Champlain College American Automobile Association.
He played for Montreal Impact"s junior affiliate, Trois-Rivières Attak, in the Canadian Soccer League in 2009, scoring 3 goals in 18 games, prior to formally joining the Montreal Impact Academy in 2010. Cossette was called up to the senior Montreal Impact squad in the summer of 2010, and made his debut for the team on July 3, 2010 in a game against the Rochester Rhinos.
