1880-1910 T.A. Smith & Son Undertakers Antique Safe w/ original combination.

I can’t yet prove that the safe originated around Cottontown/Sumner County.
The strongest clues are the safe itself. The exterior is professionally lettered “T.A. SMITH & SON — UNDERTAKERS,” while the inner compartment says “HALL’S PATENT.” The latter fits the 19th-century safe/lock industry; period sources document Hall patent safe locks by the 1850s, and Hall-type security equipment was being advertised in the mid-19th century.
The promising Tennessee lead
I found a Theodore A. Smith (1827–1905) in Tennessee genealogical records. His wife was Elizabeth A. Smith (1840–1930), and the record also identifies a son, Eddie Smith.
The dates are extremely interesting because a man born in 1827 could absolutely have operated a business called T.A. Smith & Son during the period in which a safe of this style was being used.
However, I have not found evidence establishing that Theodore A. Smith was an undertaker. So I don't want to turn a promising name match into a false identification.
I also found evidence showing that Tennessee undertaking businesses of this period commonly overlapped with cabinetmaking/furniture businesses—which makes sense because early undertakers often manufactured or supplied coffins. For example, an 1880s Tennessee history specifically identifies cabinetmakers who were also undertakers. This helps explain why an undertaker would have owned a substantial business safe like yours.

Dating
Looking at the photographs together with the historical material, I'd currently estimate:
approximately 1880–1905, with the 1890s being a particularly plausible period.
That's not yet a manufacturer-confirmed date. The construction, elaborate Victorian cast decoration, hand-painted/gilded lettering, inner Hall's Patent compartment and mechanical combination lock all point in that general direction.
The wording “Undertakers” rather than “Funeral Home/Funeral Directors” is another useful period clue. Historical funeral-home records describe the profession as being called “undertakers” in the late 19th century; one documented family business describes its operations in 1886 using exactly that terminology.