Dear Mr. Mansfield,
Thank you for posting your request on History Hub!
The Federal Government does not ordinarily create or maintain birth, death, marriage or divorce records. Such records are made and kept by State and local governments rather than the National Archives. We suggest that you search the New Hampshire, Town Clerk, Vital and Town Records, 1636-1947 FamilySearch index and request a birth record search from the New Hampshire Vital Records State Department of Health. In addition, the FamilySearch research wiki for New Hampshire Vital Records may be helpful.
We hope this is helpful. Best of luck with your research!