Tom Bombadil says this to the hobbits, in reply to the question "who are you?":
(...) But you are young and I am old. Eldest, that’s what I am. Mark my words, my friends: Tom was here before the river and the trees; Tom remembers the first raindrop and the first acorn. He made paths before the Big People, and saw the little People arriving. He was here before the Kings and the graves and the Barrow-wights. 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.
So basically, he was here before everything else. After Helm's Deep, when a party rides to Isengard, Gandalf says this to Théoden:
Well, Théoden, will you ride with me to find Treebeard? We must go round about, but it is not far. When you see Treebeard, you will learn much. For Treebeard is Fangorn, and the eldest and chief of the Ents, and when you speak with him you will hear the speech of the oldest of all living things.
Maybe this is just an inconsistency not intended by Tolkien, I don't know. A few years ago, I read somewhere that Tom Bombadil is not "a living creature" in a traditional sense, but there wasn't a strong argument supporting that. What is your take?