While there are various cat species with saber-like teeth, including the Scimitar-toothed cat (Homotherium), they also went extinct long before the 1600s.
Were there any saber-tooth tigers in the 1600s?
No, saber-tooth tigers (specifically, the Smilodon genus) went extinct around 10,000 years ago. The 1600s were well within the time period of modern humans, long after saber-tooth tigers disappeared.