For birth records I believe you are out of luck - South Carolina is one of the states that does not have birth records online. It appears the state did not start issuing birth certificates until 1915 (which are available only to immediate family members), so I do not know whether birth records even exist for Anderson County prior to that (if so, there is no evidence in familysearch.org of any availability).
If it were a well-to-do family, one might look to probate or land records; however, the father in the 1910 census record was a tenant farmer, so that is not likely to help. Thus, given that the 1910 and 1920 censuses indicate a large family, I would look for obituaries of any of her siblings naming a Mrs. Mattress as a surviving sibling. No guarantees, though, that you will be able to find obituaries (at a site such as newspapers.com, or incorporated in a memorial at findagrave.com).