The island with the earliest archaeological evidence of cats living closely with humans is Cyprus.
At the Neolithic site of Shillourokambos, archaeologists found a cat deliberately buried near a human grave. The burial dates to roughly 9,500 years ago, around 7500–7200 BCE, making it far older than the familiar Egyptian images of domestic cats. Because cats were not native to Cyprus, people must have transported the animal there from the mainland.
The find does not prove that fully modern domestic cats had already evolved on Cyprus. The remains resemble the Near Eastern or African wildcat, the ancestor of today’s domestic cat. It is better understood as evidence of an early human-cat relationship, possibly involving taming or commensal living around farming settlements.
This is why Egypt is sometimes given as the answer: ancient Egyptian culture is strongly associated with cat domestication, worship, and artistic depictions. Archaeology now indicates that cats were interacting with people in the Near East and on Cyprus thousands of years earlier, before Egypt became the best-known center of feline culture.