I think they take hundreds, perhaps thousands, of years to grow above the ocean's surface. This is what's happening right now off Hawaii with the slow birth of a new island to be called
Loihi.
Surtsey, a bit of the Mid-Atlantic Ridge which just didn't know its place, took a couple of days to form. Stuff was growing on it in less than a year.
When the Beagle was anchored in the bay at Valparaiso, there just happened to be a geological disturbance which raised the level of the rocks around the bay by at least a foot. One of Darwin's backers was Lyell, a champion of the new theory of Uniformitarianism. This postulated that the forces which had formed the landscape were still at work, and hadn't stopped with some ancient catastrophes, as believed by the Neptunists (catastrophic floods) and Plutonists (catastrophic volcanism). The idea of erosion, wearing down everything up to and including mountains, was obvious enough, but orogenesis - mountain building - was not so easy to envision. Darwin, on the Beagle, witnessed it in action (... lucky bastard, I'd say ...).
The geology of the Hawaiian chain is a bit specialized. There seems to be a fixed hot spot in the mantle, and as the earth's crust slowly drifts over it, the area over the spot becomes volcanic, and an island forms. After the bit of crust with the island on it moves off the hot spot, the island - really the top of a heavy mountain - starts to subside, partly from erosion but mainly from its own weight causing the crust under it to slowly sag. The chain is quite long, stretching to Midway and maybe beyond, so whatever's been happening there has been happening for quite a while.