Šín started his career at local side Polanka, and spent a season with Vítkovice before joining Baník Ostrava in 2014.[2]
In June 2022, shortly after his eighteenth birthday, Šín was diagnosed with testicular cancer, and immediately underwent surgery.[3] He had featured for the first team and reserves of Baník Ostrava at the time, having made his debut at the age of seventeen, but had to put his career on hold as he underwent post-operative treatment, and was unable to partake in any strenuous activity, such as football.[4]
In October 2022 it was announced that Šín had overcome the cancer, and had begun training individually, with the hope of returning to his former club Baník Ostrava.[5] Later in the same month, he sent a message of support to compatriot Matěj Pinkas, an ice hockey player of the same age who was also suffering from cancer at the time.[6]
Šín returned to first team training with Baník Ostrava in January 2023.[7] The following month he scored his first goal for the club, though it was a consolation goal in a 2–1 away loss to Zbrojovka Brno.[8] Just over a week later, he signed a professional contract with the club, keeping him with Baník Ostrava until June 2025.[9][10]
International career
Šín has represented the Czech Republic at under-16, under-18, under-19 and under-20 level.[1]