Would her marriage certificate also provide identifying information about who her parents were, providing that connection?
SS-5 application in the US? Good official sort of document. Harder to get these days - should have place of birth on it and parents. You may need proof of her parents' deaths to get a version without half the info blacked out.
Depending on their religious affiliation - something like a confirmation record in the US?
It is likely that she used an affidavit when she needed to prove birth info, or had some documentation from the family's immigration to the US that served the same purpose as an actual birth record.
