By Wikipedia's count, dozens: https://en.wikipedia.org/wiki/List_of_flood_myths

Quite a few across a wide geographic range all identically feature a handful of humans (and possibly animals and/or plants) being forewarned of an impending flood, building boats (or otherwise being put in boats), and surviving until the waters receded. (EDIT 2: I realize now that I got things mixed up and you were asking for the "Earth started off underwater" myths, but there are plenty of examples of those, too).

EDIT: to elaborate further on some specific examples (pulled from Wikipedia, except for the African example which I pulled directly from the cited source, since the article didn't include synopses of any of those examples):

- North America (Hopi): « The other version [of the Hopi story of their entrance into the "Fourth World"] (mainly told in Oraibi) has it that Tawa destroyed the Third World in a great flood. Before the destruction, Spider Grandmother sealed the more righteous people into hollow reeds which were used as boats. On arrival on a small piece of dry land, the people saw nothing around them but more water, even after planting a large bamboo shoot, climbing to the top, and looking about. Spider Woman then told the people to make boats out of more reeds, and using island "stepping-stones" along the way, the people sailed east until they arrived on the mountainous coasts of the Fourth World. »

- South America: « "The Inca’s supreme being and creator god, Con Tici (Kon Tiki) Viracocha, first created a race of giants, but they were unruly, so he destroyed them in a mighty flood and turned them to stone. Following the deluge, he created human beings from smaller stones. "In other versions of this story, the impious race is the pre-Inca civilization of the Tiahuanaco Indians about Lake Titicaca, the large high lake in the Andes. Viracocha drowns them and spares two, a man and a woman, to start the human race anew. Some versions of the Unu Pachakuti have the surviving man and woman floating to Lake Titicaca in a wooden box." »

- India: « Matsya (the incarnation of Lord Vishnu as a fish) forewarns Manu (a human) about an impending catastrophic flood and orders him to collect all the grains of the world in a boat; in some forms of the story, all living creatures are also to be preserved in the boat. When the flood destroys the world, Manu – in some versions accompanied by the seven great sages – survives by boarding the ark, which Matsya pulls to safety. »

- Korea: « Namu Doryeong (Hangul: 나무도령, Hanja: --道令) is a myth about the son of a guardian tree spirit. The son, Namu Doryeong, survived a flood by floating on the tree. He first saved a colony of ants from the flood, then a swarm of mosquitoes, until he had saved all the animals of the world. Namu Doryeong finally saved a young human boy, despite the tree's advice against it. After the flood, Namu Doryeong met an older woman and her two daughters on Mt. Baekdu, where they had been safe from the flood. The woman told Namu Doryeong if he won a contest, he could have her daughter's hand in marriage. Namu Doryeong won the contest with the aid of a swarm of ants, who turned out to be the very ants that Namu Doryeong had saved during the flood. Namu Doryeong and the human boy married the two daughters, and they formed the next race of humans. »

- Scandinavia: « According to the Gylfaginning section of the Prose Edda by Snorri Sturluson, Bergelmir and his wife alone among the giants were the only survivors of the enormous deluge of blood which flowed from Ymir's wounds when he was killed by Odin and his brothers Vili and Vé. They escaped the sanguinary flood by climbing onto an object and subsequently became the progenitors of a new race of Jötunn. »

- DRC (Bakongo): « An elderly woman, tired and covered with sores, arrived at a town in a valley. She asked for hospitality but was turned away at every home except the last one she came to. The people there took her in and cared for her until she was well again. When she was ready to leave, she told her hosts to come with her. Because of the other inhabitants' lack of hospitality, the town was cursed, and the Supreme God, Nzambi, would destroy it. The night after they left, heavy rain fell, turning the valley into a lake. All of the townspeople were drowned. »