There probably is no birth record.
Many people born in the 19th Century did not have official birth records, especially if they were born at home. Reporting births did not become commonplace until the 1930s.
None of my grandparents, all born in the 19th century, had birth certificates. None of my uncles or my father, born in the 19th and early 20th centuries, had birth certificates.
My mother was born premature in a hospital in 1917 and she had a birth certificate because she was born in a hospital.