This is going to depend on how we define music, as pointed out above.
The answer, for me, is that human music was invented by humans.
If we want to expand our definition of music to include bird song, whale song, and plethora of rhythmic and melodic aspects of nature, I think we would end up saying that music was discovered but we'd also be washing out our definition of music. We'd just be talking about pleasant sounds...
I think the point made suggesting that music is a combination of invention and discovery, a recombining and ordering of pre-existing elements of our world is an interesting one. But isn't invention always, by necessity, an act of novel recombination and ordering of pre-existing elements?
The wheel was an invention even if it was made out of materials that already existed, right? There is an element of discovery to all invention. Yet, because the product of that invention brings into being something that did not exist in its final form before, we call this an originary act, a creation, an act of invention.