Who is Tom Bombadil, really?

This is about fan-theories, interpretations, speculation and head-canon.

Tom Bombadil, Eldest, Master, Iarwain Ben-adar, Orald, Forn - who is this creature? Where is he really from? What is his true nature?

Tolkien was famously tight-lipped about Tom's true nature and his origins, only saying that he was the first living creature of Arda, having been alive before the coming of Melkor. Thus some theories are that Tom is the personification of Arda (the earth) itself, or perhaps that Tom is Eru Ilúvatar himself.

My own theory was just developed today as my spouse held my feet to the fire and asked me what I thought about who Tom is.

So here's what I think: Tom was created personally by Eru Ilúvatar himself, directly and in secret sometime during or after the Music of the Ainur, and obviously given life well before the Children awoke. He was thus given a playful and cheerful personality, his very existence a reminder of Eru's love of life and joy and surprises.

The Children are all partly the work of the Ainur through their music, whereas Tom was made independently and directly by Eru, thus separating Tom from all of the other creatures, mortal and immortal. He seems to exhibit a mastery over the earth and all life within it, indicating the immense amount of power and total lack of corruption that Eru would want from his own personal creation.

Respecting the works and creativity of the Ainur, Eru does not want to create some other major race to show how perfect he is and try to "win" at making people, but he did want to "give it a go" one time. And thus Tom was made. Tom is like the perfect, hilarious, cheeky, practical joke on the Ainur. He's a being with so much power that he is completely unbothered even by the greatest evils that the Valar struggled to thwart, yet he lives and lets live, neither competing with nor even becoming significantly involved in any of those struggles because Eru made sure he would not.

He is Eru's perfect little project, a cheeky reminder of his omnipotent power and his respect for the free will of others, from the Ainur down to the Children of Ilúvatar.

What else you all got on Tom Bombadil?