The hobbits encountered Tom Bombadil when they were strayed in the Old Forest, who provided meals and refuge. Their savior, though, was unknown to them, until Tom revealed himself as the eldest—the first to stand in Middle-Earth. He belongs to no civilization, but to Mother Nature.
There is one attribute of Tom that is distinctive from all the other characters in the series: he has no interest in power, demonstrated through his interaction with the Ring. It did not cause him to become invisible, but it was the other way around.
Tom did the ‘impossible’.
This demonstrated that Tom was unusually indistinguishable to the Buddha (although I am aware that Tolkien neglected allegories to his mythology). Buddhists, nonetheless, would recognize Tom as an ‘Enlightened One’—one that has eliminated his earthly desires. But the Ring functions to produce desires for power. However, Tom desired nothing from it, nor was he concerned about its destructive potentials. He is neither in the good or evil ‘side’, as both sides desire power; he is the neutral force.
Tom, figuratively saying, and relating to pantheism, is ‘one’ with nature; his heart resembles more of a ‘thing’ than a ‘being’, parallel to mindless matter, which plainly lack desires.
Ultimately, one may never fathom this enigmatic invention. There exist things beyond what the mind can unravel, just as Tolkien’s God is enigmatic. How can an immortal God incarnated as a mortal man, yet be both God and man concurrently? Surely this violated the Law of Contradiction, but it was revealed to be true.
God did the ‘impossible’.
The involvement of the ‘impossible’ in Tolkien’s world may indicate that the ‘impossible’ occurred in the real world. There will be inestimable argumentations on whether Tom Bombadil is Eru Iluvatar, and whether Jesus Christ is God.