Fink began his career at a young age playing for SC Maisach. At the age of nine, he joined the youth system of TSV 1860 München. Ten years later, he played his first senior games for The Lions' reserve team. After two more years in Munich, Fink signed his first professional contract, with SpVgg Unterhaching. He became an integral part of the team, and was the top goalscorer in the inaugural season of the 3. Liga. In the summer of 2009, he joined 2. Bundesliga side Karlsruher SC. He spent the first six months of 2011 on loan at 3. Liga side VfR Aalen. In January 2012, he transferred to Chemnitzer FC. He scored ten goals in his first half a season with Chemnitz, as they briefly challenged for promotion, and during the early part of the 2012–13 season he scored his 42nd 3. Liga goal, overtaking Marcel Reichwein's all-time record for the competition.