It's important to note that the term "saber-toothed cat" is a bit of a misnomer because it includes a variety of extinct carnivores, not all of which are closely related to modern cats.
When did saber-toothed cats first arrive on earth?
Saber-toothed cats, or more accurately, saber-toothed predators, first appeared on Earth around 50 million years ago in the Eocene epoch. However, the specific "saber-toothed cat" family, Machairodontinae, emerged around 15 million years ago in the Miocene epoch.