Your search made the wrong birth date assumption:
most children given up are by teens. 1940 -1945 birth date:
https://familysearch.org/search/record/results?count=20&query=%2Bgivenname%3AFaye~%20%2Bsurname%3ARobinson~%20%2Bbirth_place%3A%22Dade%20County%2C%20FL%22~%20%2Bbirth_year%3A1940-1945~%20%2Bmother_surname%3AFaye~
One comes up: with a relative Angela...
Gloria Faye Robinson
United States Public Records