The name of the kid who first introduces this idea is Percival Wemys Madison. He is one of the littleuns. He does this in Chapter 5.
He introduces the idea while they are all having a meeting. It seems that maybe they are going to stop believing in the beast, which would be a good thing. People point out that they have been all over the island and had not seen the beast.
At that point, Percival whispers to Jack. Jack tells the rest of them that Percival says the beast comes from the sea.
In chapter 5, Ralph asserts his authority by calling a special meeting as dusk settles on the island. After clarifying rules about sanitation and the fire, he opens up the meeting for participation from the boys in order to "talk about this fear and decide there's nothing in it." His hope is that by facing the fears that the boys have had and talking through the issue rationally, they will all be able to move beyond that, pull together, and be happy.
Jack starts out, not helpfully, by acknowledging the fear and saying they will have to live with it. However, he calls on his credibility as a hunter to insist that "there is no beast in the forest." Piggy disagrees, saying that they shouldn't need to live with their fears because "life ... is scientific." He then wants to hear from the "littlun who talked about a beast" so they can convince the child he's being foolish.
First Phil comes up, and his supposed nightmare turns out to have been Simon leaving the huts during the night to go to his secret place in the jungle. Next the littluns push Percival Wemys Madison forward. He's too scared and shy to speak up, so he whispers into Jack's ear that the beast comes out of the sea. Unfortunately, this turns the tide because the argument of science cannot refute the possibility. The boys see the sea surrounding them and realize there's no way they could protect themselves from something sinister that might creep up from the ocean. From there the discussion deteriorates into talk of ghosts, Jack spurns the rules, and the boys scatter onto the beach. Ralph's good intentions for restoring happiness and order have been shattered.
The beast is being discussed in an assembly by the group of boys in the book "The Lord of the Flies." Piggy has the conch and gets aggravated with all the stories about the beast. He tries to tell them it is just like ghost stories. The littleuns push a boy forward form their group. He is a small boy and boy tries to twist away from the older boys. Piggy asks him his name. He is Percival Wemys Madison. He repeats his address. Percival tells them that the beast came out of the water. He says it in a mumble so that Ralph has to lean down to hear his words and then repeat them aloud. The child falls asleep in the grass.
Chapter "Beast from the Water" page 87.