The Big Bang is a difficult concept. It’s easy to think of it as an explosion in space – but actually it was the moment when all space and time began to exist. So in that sense I don’t think it would have made any sound – and even the first stars didn’t form for millions of years after it, so there was definitely no-one around to hear it if it did.
Interestingly though cosmologists do use sound waves from the early universe to learn about what’s happening. There is something called “Baryon Accoustic Oscillations” which is a fancy term for sound waves from the early universe. Because these sound waves caused baryons (that’s just normal matter, as opposed to dark matter) to bunch up, if you very carefully measure the locations of galaxies in the universe you can see a signature of these waves even today. Because we understand physics we know how big these waves should have been, so measuring how big they appear to be is a way to get an estimate of a distance (we get one side of a massive triangle, and the angle, so we can use trigonometry to get the long side – the distance).
Actually, I think if there was an instrument to listen to it, it would sound a bit like the wind rushing past your ears on a really windy day. Because in less than a second, all the matter and stuff in the universe expanded out from a single point to something the size of a universe, it would have to be travelling unbelievably fast!