Could Tom Bombadil's Nature Hint at the 🎶Music of the Ainur?

[Ent]

Of course, that's just what I think. I could be wrong. I haven't read The Adventures of Tom Bombadil yet (my local library sadly does not have it), maybe there are more hints about him there.

You're manifestly not wrong, if that's what you want Bombadil to be, because Tolkien himself said Bombadil is purposely an enigma, like many other things in his writing.
There is no place or way in which Tolkien clarified what his intent for Bombadil, Ungoliant, the Watcher in the Water, and many other things were intended to be.
Quite intentionally on his part.

 

[Tyelkormo the Fair]

I cannot help but wonder myself. Since you relate your post to mine by some twist I cannot possibly discern, I suggest you re-read my post.
Perhaps multiple times, until its intent sinks in.
Having done that, you'll find I've already answered both yours above, and those you've put into PM to me, by what's already been said.
(See my paragraphs #3 and #4 immediately following the bolded 'initial question.')
Though I must say, I would anticipate a digestable and understandable "explanation" (Paragraph 3) and I'm havig a bit of a hard time there...
The forest you walk with your words has many divergent paths, and I can't seem to find their intersections.

I think he set too much grass on fire.

 

[Eljorahir]

Could Tom Bombadil's Nature Hint at the Music of the Ainur?

Taking just the title question by itself, I think the answer is yes. Of course, the word “hint” means only a little bit is needed.

The music of the Ainur had the ultimate unusual power.
Tom's songs have a lesser form of unusual power.

For me, the musical commonality is enough to qualify as a “hint”.

‘I know the tune for him. Old grey Willow-man! I’ll freeze his marrow cold, if he don’t behave himself. I’ll sing his roots off. I’ll sing a wind up and blow leaf and branch away. Old Man Willow!’

‘Tom put his mouth to the crack and began singing into it in a low voice. They could not catch the words…’

‘None has ever caught him yet, for Tom, he is the master:
His songs are stronger songs, and his feet are faster.’

 

[TrackerOrc]

I have to admit that Bombadil has always been my least favourite character by a very large margin.
From the first time I read LOTR all those years ago, I just couldn't get over the doggerel verse, the talking about himself in the third person, even his dress sense.
I have no idea what Tolkien was trying to do here.
I basically just skim through the pages he appears in.