You might find luck in producing a mathematical formula/algorithm for scoring any noise on its originality (you need it to somehow compress - and compare to - all existing noises, so the main issue is collecting and labeling all of that data), then use this to train yourself to not create anything with a low score.
You need to ensure it doesn't only consider stuff like the timing/order of notes, and the like. Because speeding up or slowing down a song should not be considered making an original noise. Similarly, white noise is always unoriginal, despite there being near infinite variations of it. So it needs to also look at a more holistic view of the noise, such as statistical analysis of the frequencies to identify different colors of noise.
I think such a value function would be complex enough (how do you rigorously define originality?), that the only way to realistically achieve it, is to make it be an AI you teach - but you can't teach it directly/alone as that introduces biases, so even that is near impossible.
Either way, let's pretend you created this black box, you now are faced with the struggle of teaching yourself to do originality. Humans are not good at this, as we grew up in a world where not following teachings from others easily leads to death (like if you decide to jump off a cliff). So I suggest you then further take this value-function, and create a (secondary?) AI that generates noise. And teach it to always achieve high scores on this originality-function (remember to add the new noise it generates to the dataset the value-function uses! Or it might simply start to continuously generate the same thing all the time). Basically, you need to create a generative AI.
Then you can run this AI, to produce all the original noises we still haven't produced. Achieving our ultimate goal: ensuring all other "dudes who likes making music" are forcefully made to empathize with you! mwahaha!
ps: the above won't actually work (unless you intend to retrain it all each time you want to generate something), simply because even if you train an ai to be original, the self-referential paradox means that it will start mimicking itself. To avoid that, you somehow need to create some sort of feedback into the system that biases it away from its past works. But even then, there is no guarantee it won't simply be finite in the number of original works it can create, and that after X iterations it will simply stop being useful.
If the main problem is finding every original piece of music, you don't actually need a generative model to create every original song not made before, the self-referential problem you mentioned.
Let's look at the analog problem in language. In 1941, Argentinian writer Jorge Luis Borgés published the "Library of Babel", a story about a library containing every text ever made within a certain constraint. In this library, every book has 410 pages. Every page has 40 lines. Every line has 80 characters. And every character can be any of 25 specific letters and symbols.
You might have realized two things: (1) the library is huge, but it's actually not infinite, (it has exactly 1,956x10^101834097 books); and, (2) if you wanted to find texts longer than 410 pages, you need only to find the sequence of books that together form your longer text.
That means we now have every text in existence in a compact, finite set of books. Of course, most of it is noise, but that takes us to the next point: this is an estimation problem.
Let s(x) be the function that given a text x gives us a score k ∈ [0,1] , where k is how "human-like" a text is. Let ŝ(x) be it's estimator. You might have guessed this is the perfect task for an AI model. The AI would scourge over every single text and would report to us whether the text is human-like or not. Our task is simply to filter the ones with the highest score.
Music has the unfortunate (for us) property of living in a continuous world because pitch, or more specifically, frequency, is. But we as humans like discrete things anyway so we assign names to specific pitches. That's notes. Rhythm is also continuous but we divide it into beats (4 beats, 2 beats, one beat, half a beat, ...). We discretize it and then limit ourselves to, say, 2 minutes songs.
We now have every song ever made and to be made in human history. Your task is to train an AI model to find every song that isn't just noise, and you would find every song a human would actually listen to. A second AI would score the songs by originality, and you would have every original song never made.
Not enough computation? Limit yourself to 10 second song snippets and the property of having "every song ever made" still holds true. Now the only problem is implementation, but that's trivial, and an exercise better left to the reader.