Kaygin is a product of the youth academies of the German clubs FSV 1946 Saulheim and
Mainz 05. In the 2022–23 season, he was the second top scorer for the Mainz U19s with 22 goals in 19 games and helped them win the
Under 19 Bundesliga. On 9 June 2023, he transferred to the Austrian club
Rapid Wien on a three-year contract. He made his senior and professional debut with Rapid Wien as a substitute in a 1–0 loss to
Red Bull Salzburg on 9 December 2023. On 10 January 2025, he joined the Dutch
Eredivisie club
Willem II on loan for the second half of the 2024–25 season. On 24 June 2025, Kaygin signed with
FC Ingolstadt in
3. Liga. ==International career==