Here's a table with the US vital records begin dates for civil registrations for births by state. It can help you determine where to look.
Before that time, there may be other resources available for these vital records, but you have to contact each state to find out the details.
1. Delaware births and deaths stopped in 1863, and began again in 1881.
2. All Louisiana birth records are kept in the parish clerk offices.
3. There are no Tennessee statewide birth or death records for 1913.
Be prepared to search beyond these dates if necessary. Just because you did not find your ancestor in this US vital records begin dates search, doesn't mean they are not out there.