Birnbaum competed for the U.S. U-18 and U-20 National Team squads in tournaments in Portugal and Mexico in 2008. He was a part of the U.S. squad that competed against Manchester United in the 2008 Milk Cup Final. Birnbaum won a silver medal with the U.S. team in the 2012 Pan Am Maccabi games in Brazil.
2013: Birnbaum was one of three team captains for Cal. He was a Missouri Athletic Club Herman Trophy Semifinalist, named a NSCAA First Team All-American, NSCAA First Team All-Far-West Team, College Soccer News First Team All-American selection, All Pac-12 first team, Pac-12 All-Academic honorable mention and Soccer News Net College Boot Player of the Year Finalist. He started and played 19 games at central defense for the Bears and finished the season with 10 goals and one assist. Birnbaum helped lead the Bears to the NCAA tournament quarterfinals.
2012: Was named preseason All-American by College Soccer News, but played just two games for the Bears due to injury. He was redshirted for the season.
2011: Birnbaum was co-captain during his junior season and earned a spot on the All-Pac-12 first team and garnered honorable mention Pac-12 All-Academic status. He started in 16 games for the Bears.
2010: Started in all 20 games for the Bears and finished the season with one goal and five assists. Was a Pac-10 All-Academic Honorable Mention recipient.
2009: Made eight starts as a true freshman, which was the most at the time in school history. He appeared in 17 games.