People in my family had to bring in the family bible and letters of testimony to have BCs issued in the fifties and sixties. Born at home, no docs, no papers. Not uncommon in rural America.
Both my parents and all fourteen of my aunts and uncles were born at home, no doctor.
They never got birth certificates until they needed them as adults.
They would take the family bible, where all births and deaths were recorded, and that was enough to get a BC.
It was a different world then.