Is Tom Bombadill someone who'd get annoying?

[Radaghast]

Could be...except we only know Eru made Tom at some point; we don't know when that was... pre-Ainulindalë? post-Ainulindalë?
And here's so something to think about: what if Eru brought Tom into being during the Ainulindalë? in the midst of The Music?

Tolkien is silent about Tom's specific place in creation.
Until that unpublished (1964) letter to Prof. Przemysław Mroczkowski turned up, we always thought he was part of Eä ; but he isn't.
So we can speculate about Tom until Mount Doom freezes over 🙄, but we'll never get any closer to figuring out his origins.
Fun to do... but we end the way we begin: in ignorance.

As Tolkien put it, Tom was a character who "wanted an ‘adventure’". I think that's about all there is to it. Basically, he wanted Tom in a story. The idea to make the sequel to The Hobbit about Tom went nowhere but the desire to feature Tom in some way was evidently so strong that he just placed him right in there without any detailed explanation.