Yes. I am having the same problem with my father. He was adopted in 1913. Still do not have a definitive answer. Have you done a dna test? You will find clues there. That is my first recommendation. Then contact the Archives of the Catholic Diocese of Cleveland, 1404 East Ninth St.,Cleveland, Ohio 44114. Most likely she was baptized there and ask for a baptismal record. The names of her birth parents should be listed on it. Also email email@example.com
for a Request for Genealogical search.
Let me know if his helps!