Another similar question is: “When did cats come to Australia?”
Because the continent of Australia was cut off from mainland Asia by water there was no migration of wild cats from Asia and hence no domestication of small wild cats on that continent. Australia was entirely free of any species of wild cat or domestic cat until humans came to the continent with their cats. There are still no wild cats in Australia unless you count super feral cats behaving like wild cats.
The australia.gov.au website tells us that between 1606 and 1770, 54 ships from Europe made contact with Australia. Many were merchant ships. There is no mention of cats being brought ashore. Cook claimed the east coast of Australia on 22 Aug. 1770. Did he have a ship’s cat? Almost certainly yes. Did the cat come ashore?
The environmental department of the Australian government does speculate that ship’s cats from as early as the 17th century may have been taken ashore with European settlers. They refer to ‘Dutch shipwrecks’.
We don’t know but Wikipedia says that the first introduction of cats to Australia from settlers to that country took place in 1804. There were feral cat colonies by the 1850s. A feral cat problem was noted in the early 1900s.
In conclusion cats came to Australia on ships with settlers from Europe sometime during the period when they first came to Australia perhaps during the 17th century and then became ‘noticed’ because of their numbers in the mid 19th century.