This may seem a tad fluffy to some, and perhaps unrelated to Hellenismos to others, but it’s not. Cats are absurdly present in Hellenic mythology, associated with various deities, and the latest evidence suggests that the notion that it was Kmet where the housecat was first domesticated is wrong —the earliest evidence of housecats comes from Neolithic remains in Kypris.
It’s also easily argued that the Sphinx is a form of fantastic cat, as its body is a lion with eagle’s wings, and only its face is human. While usually depicted as female, inscriptions survive that depict Eros Areios in male sphinx form.
Dionysos is probably most famous in His associations with big cats, followed closely by Herakles and the Nemean lion / Leo. Then in Ovid’s Metamorphosis, in describing the animal forms the Theoi took to escape Typhoeus, Artemis is said to have taken the form of a cat.
Obviously, Egyptian cat goddess, Bastet, is the most famous of deities with a cat representation, and followed is Sekhmet, who had the head of a lioness. To the Hellenes, Bastet is known as Ailuros, and is considered an epithet of Atremis’ lunar aspects. The Romans associated the Norse Freyja with Venus and Aphrodite, and Freyja apparently is rather closely associated with cats, and the domestic breed, Norwegian Forest Cat, is said to be descended of Freyja’s cats; by one version, when Hippomenes won the footrace against Boeotian princess Atalanta, Aphrodite did not feel the man returned to the Goddess Her due, and so transformed the pair into lions (convention at the time was that European lions could not mate without killing eachother, so this would’ve prevented the consummation of their marriage).
By some accounts, it was a cat, and not a ferret, whose form the Theban midwife Galinthias was made into.