Koşut was born in Gaziosmanpaşa, Istanbul. He started playing basketball in Bayrampaşa Sancak team when he was ten. In 2011, he moved to the Anadolu Efes junior team.
Anadolu Efes
In the first year, he played for the junior and youth teams of Efes. He was loaned for the 2012–13 season to TB2L team Pertevniyal which is the pilot club of Anadolu Efes. In the summer of 2014, Koşut moved to Anadolu Efes first team. He was released from the team on 20 June 2016.