Eldest?

[Texadan]

Bombadil also tells the hobbits...

Tom was here before the river and the trees; Tom remembers the first raindrop and the first acorn...When the elves passed westward, Tom was here already, before the seas were bent. He knew the dark under the stars when it was fearless -- before the Dark Lord came from Outside.

If that's true, it seems Tom was there when only the Valar lived in the world. Could he have been one of them? His power and joy is in singing and it was through singing the song of Ilúvatar that the Ainur, which included the Valar, made the world.

And, to be a bit facetious, Gandalf did say that Treebeard was the oldest thing that walked the earth. Bombadil never walked. He hopped; he jumped; he danced.