Dear Robert Rabiola,
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.
For more information on conducting genealogical research within our records, please visit our webpage: https://www.archives.gov/research/genealogy.
If you haven't done so already, I would check the Census records https://www.archives.gov/research/genealogy/census/online-resources. A precursory search on Ancestry shows a Henry Cochran married to a Margaret Holsomback in the Census starting in 1900 (in Shelby County). Under normal circumstances, you could access this information without an account at a National Archives facility, but they're closed currently due to the pandemic. Many libraries offer this access as well. You may also be able to find the info on Family Search or other services in the link above. .
Unfortunately, birth records, especially in rural areas were spotty at best. Outside of church records and family bibles, there is often little to be found. I would also check with the Shelby County Historical Society and Museum here: https://www.shelbycountyhistory.com/
We hope this information is helpful in your research.