Hi again Elizabeth,
I found a birth certificate on Family Search for the birth of an unnamed son of EJ Smith and Lillie Parsons on 8 April 1912 in Stacy, McCulloch County, Texas. The unnamed son is my great grandfather, "Davey/Davy Stirman Smith." Here's the citation for it:
"Texas Birth Certificates, 1903-1935," database with images, FamilySearch(https://www.familysearch.org/ark:/61903/3:1:S3HY-61D9-3G2 : accessed 27 October 2023), certificate image, unnamed Smith, 8 April 1912, certificate 49589; Texas Department of Health, Austin.