Yes, humans and cats do share a common ancestor, though you have to travel very far back in time to find it.
All life on Earth traces back to a single-celled organism that lived billions of years ago. More specifically, humans and cats are both mammals, meaning we descend from a common mammalian ancestor that lived roughly 200 million years ago.
It may come as a surprise, but cats are actually more closely related to whales and hippos than they are to humans. Over millions of years, mammals diversified into countless forms, leading to the wide variety of species we see today.
The most recent common ancestor of humans and cats is estimated to have lived about 85 million years ago. This small, furry creature was likely active during the day and gave rise to two very different evolutionary branches.
While we do not share a recent ancestor, humans and cats are still part of the same broad animal group—mammals—and remain connected by an ancient lineage.