Daştan first learnt to play chess at the age of seven. A year later, he won the Turkish U8 Championship. He went on to win multiple Turkish youth championships, including the U10 Championship in 2008, the U12 Championship in 2010, and the U14 championship in 2012.

Internationally, Daştan has also performed well, with notable results including a shared first place in the U12 division at the World Youth Chess Championship in 2010. He also secured shared third place at the 2015 Izmir Chess Festival.

Daştan has represented Turkey at team events as well, playing on the Turkish team at the European U18 Team Championships in 2012 and 2013, as well as the European Team Championships in 2017. He has been coached by Turkish International Master Ekrem Cemil Kılıçarslan.