Özdoğan started playing youth football at BK Avarta. He moved to Kjøbenhavns Boldklub (KB) in 1999, the reserve team of multiple Danish champions F.C. Copenhagen (FCK). Özdoğan made his debut for F.C. Copenhagen, the defending 2006 Danish Superliga champions, in the unofficial 2006 Viasat Cup tournament in May 2006, after playing the first half of the 2006–07 season in the KB youth team, he was a part of the FCK squad for the Scandinavian Royal League 2006-07 tournament. At new year 2007 he was promoted to the KB senior squad, two years early, alongside Mads Laudrup.