Dear Mr. Graham,
Thank you for posting your question on History Hub.
The Federal government does not ordinarily create or maintain birth, death, marriage, divorce, adoption, or burial records. Such records are made and kept by state and local governments rather than the National Archives.
We hope this information is helpful.
The National Archives and Records Administration
Guernsey Co Ohio began keeping birth records in 1867. A substitute for civil birth records would be baptismal records, if you can determine the church where he might have been baptized.