The birth record referenced in the profile is as good as it gets since church records were the only such records before the 1870's. The best, albeit not free, source for protestant church records would be Archion, they let you search for free but charge a fee for the actual record if you find one.
And his name was Gottlieb Ludwig, not Gottlob, and German culture does not have the concept of "middle name" meaning Ludwig should be as second name in the "First Name" field.
Nürtingen in 1834 was politically not connected to Esslingen, Baden-Württemberg did not exist until 1952, neither did Germany until 1872. It was its own Oberamt, the equivalent of a county, in the Königreich Württemberg, a sovereign member of the Deutscher Bund.
