Günsür was born in 1975 as the second child of a family of Tatar descent (a Turkic ethnic subgroup).

[2][3] His mother, Sibel, was a lecturer and his father, Teoman, was an industrial engineer who graduated from the Middle East Technical University and worked in a number of different sectors.

[3] His older sister Zeynep Günsür Yüceil, who is a choreographer of modern ballet, is also a lecturer.

At the age of 14, he appeared in Okan Uysaler's seriws Geçmiş Bahar Mimozaları with actors such as Rutkay Aziz, Filiz Akın and Müşfik Kenter.

[3] Günsür gave concerts with a music group and ran a restaurant for four years.