If there were birth records, they would be held by a church. North Carolina didn't start recording birth certificates regularly until 1913.
If they attended nearby Mt. Elim Church, I don't recall any (or many) births being recorded in their church minutes. I will have to check at a later date.
Also, there was a Josh(ua) Shepherd that married Sarah Ann Nye on April 18, 1856. This could possibly really be his mother. In the 1900 census for Ferdinand, his birth is giving as May 1856.
I have been looking, however, and he is not in Josh and Sarah's household in 1860 or 1870.