Sine waves form one of an infinite number of basis functions which you can map a continuous function onto. They’re super popular because the F in FFT means Fast and it’s not a joke.

By way of your friend and mine the laplace transform, you can roughly show that the fourier transform is a special case of a whole family of maps.

so yes, it’s sine waves all the way down, but it’s one of any number of other handy friends all the way down, too.