Born in Ruma, he started his youth career in a local club called FK Ajaks from Novi Sad where he played between 2003 and 2005.
After the Pećinci based club earned promotion to the Serbian First League, Šušnjar extended his loan for the 2011–12 season.
Halfway through the season, he returned from Donji Srem, and was then loaned to Montenegrin club Sutjeska Nikšić, where he spent the rest of 2011–12 season, establishing himself as one of the key players in team's successful attempt to avoid relegation.
In 2008, Šušnjar has represented Serbian under-17 team during the qualifying round for the 2009 UEFA U-17 Championship.
He played three matches, scoring a brace against Moldova and one goal against Sweden.