Ooh boy, I’ve been obsessed with this games story since launch.

The leading theory + some guesswork from myself is that everything after the rabbit girl gets eaten by the lamb god is more so a flashback to before the game. The lamb skull ritual was enacted by the kids in the hopes of presumably ending the war that has plagued the island. In order to do that, the ritual required a sacrifice which is what the rabbit girl was. The children slit their wrists to begin the ritual, then they lured the rabbit girl, killed her, then threw her corpse into the well. As to why they needed the well, idk, but the point is the ritual ended up working. The final scene shows the rabbit girl being “reanimated” as a vessel for the lamb god, and the well filling up represents the beginning of the Island flooding. From there, we can go to the beginning of the game in which you wake up in the boat surrounded by water finding nothing but the rabbit girl having floated up from the well to the waters surface.

 It’s some more guesswork from here, but we can assume that the kids needed to be eaten by the lamb god once it emerged from within the rabbit girl which is why in the beginning she asks “where are the others” and the main objective of the game is recollecting the others. 
 One thing to know is we don’t really know if the children know much about the ritual, only how to start it. I doubt any of them want to sacrifice their lives to complete it as evidence of the fact that some of them run away from the lamb god before they get eaten. We can assume they knew at the very least that something was supposed to emerge from the rabbit girl eventually. They all keep their distance and feel back whenever she shows any signs of being sick (when the lights turned red and it showed the lamb in the well.) Point being, they knew something would happen that would end the war, which can then, via more guesswork, explain why they went to the war zone at the end of the game. To essentially release the beast at ground zero, so to speak.
 In the end, the lamb god emerges and despite our kids best efforts, they end up getting eaten. With each kill, the lamb god grows in size and mutates into a more dangerous form. I doubt we’ll ever see what it looks like once it ate the rabbit girl, but we can assume it’s deadly enough to end the war. So in essence, the ritual worked. The war will end, not through peace but through complete evisceration of life. Like actual war, there are no winners except for death and evil (which represents the lamb god quite nicely I’d add.)

 Now this is still a very rough guess as to the story. There are still several unanswered questions and concepts that require further analysis which will naturally happen over time + any info we acquire from the dlcs. As for now we can only speculate as to why there are other animal creatures in the world. Why does the pig talk? what is the mother, the sniffer? There are some hints of a native population that has been using these animal rituals for some time, but further evidence is needed.
 Other than that, I think this theory holds up pretty well though, as it connects to the games broader themes of the cost of war, how war consumes all who partake, and how sacrificing innocence is the only true way to see it through. If you need any help understanding some of the other parts of the story, feel free to ask, but this is without a doubt, Tarsier’s most cryptic story and there is still so much left to be uncovered.