After attending elementary school and graduating from high school in Munich, Fink embarked on a degree in philosophy, religion, science, and the History of Art at the universities of Munich and Marburg and was subsequently awarded a Doctorate in Philosophy.
Following his academic career Fink worked in a bookshop and a scientific library, rising to the position in the latter field of chief advisor.
Following the bombing of Germany by Allied forces, Fink relocated to Postmünster, a municipality in the district of Rottal-Inn, Bavaria.
After the Second World War he re-established his political career through joining the CSU in 1946 and representing this party as District Chairman.
In Parliament Fink was a member of the Föderalistischen Union (FU) and became the lead parliamentary administrator of the group within the Bundestag.