Where did Hobbits come from?

[Lord of the Mark]

I was just reading the Fellowship of the Ring for the fifth time and I came to In the House of Tom Bombadil, and there Tom's talking about how he was there when the first raindrop fell, the first acorn, and he made paths before the big people, and he saw the Little People arriving. The Little People arriving. That implies that Middle-Earth was there before Hobbits were, that also implies that Tom knows about goings on in all Middle-Earth, so if the Little People were "arriving" then that means that they must have come from somewhere over the Sea, but not from Numenor otherwise there would be a record, so that means that there's another island out there. The Home of the Hobbits.

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