Tolkien gives a comprehensive account of the great deeds and events of the three ages. He does not fully preclude the possibility of other entities arising outside the history he provides. The origin of the ancient Ents, for example, remains a mystery. Where and from what Tom Bombadil came I believe was meant to remain a mystery for ever ("forever" outside Tolkien-speak), adding to the mystery and depth of the world Tolkien creates.
Eventually, it would all become boring if Tolkien's written history covered all that transpired in the world he creates.
I just think it is fun to speculate about it.
BTW, I think The Silmarillion talks about guardian spirits from Yavanna, the Valar in charge of plant life, entering into the trees long before the Elves awaken. Obvious possibiities there involving the Ents.