1600 BCE. The Lapita culture (defined based on pottery) starts showing up on the islands of Melanesia around this time. The culture was almost certainly brought from outside, by mariners speaking an Austronesian language (Proto-Oceanic), who traced their roots back (immediately) to island Southeast Asia, and (earlier) to Taiwan. The nearer islands of Melanesia were already inhabited when the Lapitans arrived, by people similar to modern New Guineans, whose ancestors had been there for tens of thousands of years.
The Lapitans had advanced sailing skills, and also introduced some domesticated animals – pigs and chickens. But they don’t seem to have had a huge demographic edge over the earlier inhabitants, who had already developed agriculture on their own, and may have had more resistance to local diseases like malaria. The Lapitans mostly settled smaller, harder-to-reach islands, and established enclaves on larger islands.
Eventually the descendants of the Lapitans would go on to colonize much of the Pacific. The genetics of modern Pacific islanders tells us some things about their ancestors’ stay in Melanesia. The Lapitans picked up some DNA from earlier Melanesian inhabitants. And, interestingly, this gene flow mostly involved Lapitan women and Melanesian men. So the Lapita story is not a story of new guys invading, steam-rollering the locals, and taking their women, as happened in lots of other places. It is maybe more a story of lonely sailors’ wives not always behaving like Penelope, the legendary faithful wife in the Odyssey.