My grandmother was born in a county in Iowa where the courthouse and all its records, including her birth record, were destroyed in a fire. She had to jump through some hoops to get it, but the State of Iowa eventually issued her a delayed birth certificate based on some entries in a family Bible and public school records.
My grandmother (born in Texas 1902) never had a birth certificate so when she applied for social security in 1960/61, she had to rely on witness statements and a copy of the family bible birth record to be eligible. That info was accepted.