Don't confuse the discovery with the use. "C-14 dating" was not used until it was found to have a suitable half-life and presence in organic materials.
All chemical phenomena are empirically determined by observation. Until the existence of radioactivity was known, and later, the abundance of isotopes for many elements, the idea or computation of a "half-life" was unknown.
After experiments determined the existence and consistency of a radioactive "half-life" it could be applied to archaeological and geological dating. Carbon-14 is an excellent element for large time spans with organic materials. It isn't very accurate for short time periods.
Before the discovery of isotopic element dating, there really was no way to have any idea of the ages of materials, rock layers, or sediments. Some approximations in near-history could be done from written documents, but before written records existed we could not estimate the age of a particular material.