This is a very interesting issue.

My father past away almost 30 years ago at age 65. Prior to marrying my mother, he married another woman and had a daughter from her, then divorced.
He never really spoke about that marriage, but we know it occurred at approximately 1939.
We suppose the marriage was in NYC district, which he lived his whole life.

We're anxious to find out who is (or was) our sister.

P.S. our family name is very distinctive, might that help to find entries in the various archives?

What actions can I take to find out about his marriage?

Not that I have much, but I'll provide more specific info on demand.