The cynodont cited as the earliest suggested example of hibernation, about 252 million years ago, is Thrinaxodon.
Thrinaxodon was a small, fox-sized cynodont that lived in the Early Triassic, shortly after the Permian–Triassic extinction. Fossils from South Africa and Antarctica show that it dug or occupied burrows. Some specimens were preserved in tightly curled positions inside burrows, prompting the idea that this mammal relative may have used seasonal dormancy to survive harsh conditions.
The wording “suggested example” is important. Fossils rarely preserve behavior directly, so researchers infer hibernation or torpor from clues such as body posture, burrow use, anatomy, and growth patterns. Thrinaxodon is therefore an early hypothesis about hibernation-like behavior, not proof that it hibernated exactly like a modern dormouse or bear.
A common mix-up is Lystrosaurus, another synapsid. Research published in 2020 found growth patterns in Antarctic Lystrosaurus tusks consistent with repeated metabolic stress and a hibernation-like state around 250 million years ago. That is often described as the oldest direct fossil evidence of vertebrate torpor, but Lystrosaurus is a dicynodont rather than a cynodont. For the question’s specific historical wording, Thrinaxodon remains the canonical answer.