There are still problems with the explanation you gave. If your father was born in the year 1931 in Linz, then his birthplace was in Austria. Hitler was not even a German citizen yet. He and his NS party came to power in Germany a few years later. The "Anschluss" of Austria happened in 1938.
If your father was born in Linz in 1931, he cannot have been born in a baby-farm (provided baby farms existed at all). It could have happened in or about 1941.
Have you a birth certificate (or christening document) of your father. Was he Roman-catholic? In Austria, the religions recorded vital events on behalf of the state until 1938. What does the birth certificate say about the father of the baby? If you or your family does not have a birth certificate of your father, you would need to locate his birth record in one of the parishes of Linz. You should then also enquire whether there exists a "Pflegschaftsakt" (file about the government's care of the child, such as name of the father for alimony payments, name of the legal guardian, name of the foster family unless the mother was able to provide sufficient support herself). I would ask the State Archive of Upper Austria about locating the Pflegschaftsakt.