Sea levels vary, notably falling during ice ages. For a map showing coastlines during the last glacial maximum, 22,000 years ago, see
This was the last peak in a cycle of glaciation and thawing lasting from about 100,000 years ago to about 10,000 years ago, which covers the times in which many land masses which are currently isolated were reached. At the time, many of these land masses were not isolated, and people simply walked. For example, North America was connected to Siberia by dry land, and the Americas were probably first settled by people walking from Siberia (accompanied by their dogs). Britain was settled multiple times by people who walked. The earliest settlement of Britain, almost 1 million years ago (by Homo erectus if you're a "lumper", and Homo antecessor if you're a "splitter") didn't depend on ice ages, since at that time, Britain was permanently connected to the mainland by land that would have been above current sea level. This connection was broken about 400,000 years ago, and ice ages after that resulted in repeated abandonment and resettlement of Britain, all by foot. The North Sea is shallow, and Britain only achieved its current separation from the mainland in the 6th millennium BC.
However, walking was not the only method of settlement. There are many cases where the first settlement was by boat. The earliest definite case of settlement by boat is Australia, first settled about 60,000 years ago. About 60,000 years ago, it was possible to walk most of the way from Eurasia to Australia. Sea levels were much lower, and many of the present-day islands were part of the mainlands. For example, the Sunda Shelf was dry, and Sumatra, Java, and Borneo were part of mainland SE Asia. There were water gaps that needed to be crossed, either relatively small gaps from the mainland and then island-to-island until Timor was reached (the possible southern route for the the first settlement of Australia), or a short hop from the mainland to Sulawesi, and then island-hopping to western New Guinea, which was connected by land to Australia (the possible northern route). The biggest gap along either of these two routes was about 90km, from Timor to Australia. While it would not have been possible to see the Australian mainland from Timor (even with the lower sea levels of the time), there were offshore islands that should have been visible from Timor, and crossing from Timor to Australia was possible without ever being out of sight of land. The northern route, through Sulawesi to New Guinea, has a shorter longest gap, and it was possible to sail along that route without passing out of sight of land. Being able to keep land in sight makes for much safer sailing, since return to the starting point is much simpler than if one goes out of sight of land. If the settlement of Australia was through Sulawesi, Sulawesi would have been reached by boat, but we don't know the early route to Australia, and the first settlement of Sulawesi is not reliably dated (Sulawesi was settled by 30,000 years ago and probably by 50,000 years ago, but this is later than the probable settlement of Australia).
There are many later cases of settlement by boat, including Mediterranean islands, and the settlement of Polynesia, which was spread over more than 2,000 years, beginning by 1,000BC, and finishing with the settlement of New Zealand about 1300, only 300-350 years before the European discovery of New Zealand. The last two major island settlements before New Zealand appear to have been Iceland in the 9th century, and Madagascar probably about 1,500 to 2,000 years ago.
The later settlements used sophisticated boats, capable of sailing long distances. Early settlements used simpler boats, probably paddled rather than sailed. No boats even close to the age of the oldest settlements have been found. It is often suggested that the earliest boats were dugout canoes, where a tree trunk is hollowed out to make a canoe. Another candidate is sewn-bark canoes, which have a long history of use in Australia:
and appear to predate dugout canoes, which are only known to appear after iron axes became available (through contact with Sulawesi). While making dugout canoes with stone tools is a formidable task, fire can greatly reduce the labour required, and dugout canoes are a possibility (the oldest boat ever found, the Pesse canoe, about 10,000 years old, was a dugout). Bamboo and log rafts are other possibilities, and also reed boats. For photos of many of these types of boats, see
Boats appear to have a very long history, probably pre-dating Homo sapiens by over a half-million years. Flores (in Indonesia) and Luzon (in the Philippines) appear to have been settled about 700-800,000 years ago, by Homo erectus, so water barriers of up to about 100km could be crossed at least that early. The great advances made much later by Homo sapiens included sails, reducing the dependence on muscle-power and currents, and (probably) navigation allowing safer sailing out of sight of land.
Further reading:
On the settlement of Australia:
On the settlement of New Zealand:
In a splendid piece of experimental archaeology, two replica canoes sailed from Polynesia to New Zealand in 1985. The sailing of the Hōkūle‘a from Raratonga to new Zealand, as reported in
Early settlement of Luzon:
Parts of this answer come from my past answer in https://www.reddit.com/r/AskHistorians/comments/dgtybm/why_did_it_take_so_long_for_the_m%C4%81ori_to_arrive/
