I'm currently watching The History of Future Folk, which is about an alien who comes from a planet that never had music. This got me thinking, has there been a culture that never created music?
In short, no. I mean, there may have been primitive cultures that have no music at all, and certain societies have banned music outside religious practices, or banned it within religious practices, and some have developed more rhythmic music, or vocalizations, but that are still musical. But if there is a culture that, throughout its history, have never developed any form of musical expression, I've never encountered it.
As far as we know, no. The anthropologist Donald Brown has compiled a list of "human universals" which are found in all human cultures with no known exceptions. It includes the following entries (here copied from the appendix in Steven Pinker's The Blank Slate):
r/AskAnthropology might be able to help out with this one.
Well, to add to what others have said, there is also the problem of actually properly defining music. Traditional definitions, like Varèse's "what is music but organized noises?" is, while expansive in its own contemporary context, highly lacking and leaves out much of music and philosophies surrounding music that falls outside of the audio-centric, mostly Western music tradition. For example, would you view buddhist meditation bells as music, since the function of the sound is completely different than what is generally considered music? Musicology have had a longstanding problem with being ingrained with a eurocentric view of music and its function, even up until today. It is partially because of this that in reality, musicology can almost be viewed as a young field of research when it comes to questions like yours.
I have in my studies yet to come across any really satisfactory answer from anyone to questions like these, but the most interesting lead I know is that it is starting to interest linguists who are interested in the birth of language. What is the difference between language and music from a biological standpoint? Did language develop evolutionarily by itself or in tandem with music, are they separate or codependant?
Furthermore, besides overlapping with language, there is the whole deal of understanding the separation and interlapping between music and art. Is all music art? Is art in one culture the same as art in another culture, or even can music not be art in one culture but viewed as art in another culture? And is what one would consider music in one culture just the noises of a ritual in another cultures?
To sum up, here's two possible direct answers to your question:
"It might have developed in prehistory or before mankind, before cultures."
"It depends on if you would consider another cultures music as music by your own definition."