I had a lot of questions as I re-read Tom Bombadil passages for the first time in years....I felt a lot were answered in the well-thought-through https://www.cas.unt.edu/~hargrove/tombomb.html -- by someone who obviously has read his Tolkien (and not just the most famous bits, let alone not just has seen some movies!). Many thanks to Dr. Hargrove!
Update: But how does one believe that (inasmuch as one believes in a fictitious universe) if one (of course!) believes Gandalf when he says that the ent Fangorn is the oldest thing walking Middle Earth? ("Treebeard is Fangorn, the guardian of the forest; he is the oldest of the Ents, the oldest living thing that still walks beneath the Sun upon this Middle-earth," from "The White Rider" chapter in The Two Towers, J.R.R. Tolkien) Perhaps Tom Bombadil is not counted as a "thing," and ents are in that it took elves to wake them up??? (as explained by Fangorn in the same book). More to the point, see "Of the Ents and the Eagles" in The War of the Jewels, where we learn that the ents were sort-of originally things. (I don't want to spoil that bit for you if you haven't read it yet.)
...Yet another update as I finally finished Dr. Tolkien's letters volume. Tom Bombadil is meant to be an enigma, per letter 144.