Welcome to History Hub,
That's a hard one.
If it was me I would take a DNA test on a genealogy site and
wait and see what pops up.
Good Luck in your search
Dear Ms. Cohen,
Thank you for posting your request on History Hub!
In addition to the information from the previous poster, we suggest that you begin your research by reviewing the FamilySearch Research wiki for United States Adoption Research as well as the unofficial website GI Trace.
Questions concerning a former member of the U.S. Armed Forces who may be the father of a child born during or around the time of World War II should be sent to the NARA's National Personnel Records Center, (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002. Please mark the envelope and the letter "War Baby."
Due to the COVID-19 pandemic, the NPRC was closed from March 23 through June 23, 2020. As of June 24, the NPRC entered into Phase One of a gradual reopening process. On October 5, NPRC entered Phase Two. The center is currently only servicing emergency requests associated with medical treatments, burials, homeless veterans, VA Home loan guarantees, and employment opportunities. If this is urgent, please see Emergency Requests and Deadlines. We apologize for any inconvenience.
We hope this is helpful. Best of luck with your family research!