A very quick search shows crossbows in the 300-400fps, longbows in the 250fps range. Most siege weapons are designed more for weight of projectile than speed, so I doubt they're going to be faster than that.
Which is well short of the 1125fps that is the speed of sound.

Black powder rifles easily hit 1500fps at average loads.

Cannons I'm having a hard time figuring out real numbers, most of what I see so far are math problems, so designed to teach math rather than trying to be realistic examples (as in they all use nice round numbers). But we can probably assume that no matter what they did on average, someone decided to pack enough powder in to go faster than mach 1, even if it blew up and killed them in the process. Cannons have existed since the 12th century.

Of course gunpowder itself is from the 9th century, and chances are they accidently made things blow up with that. And probably saltpeter before that. As well as who knows what else when they were messing with chemicals. There are also completely natural gasses and powders that will explode with flames that they could have accidently done many times.
Even grain dust can be explosive in the right concentrations, and we've been making grain for a very long time, so it's anyone's guess as to the first time the circumstances were right for that to happen.


If you want "on purpose" and "with some regularity" I would say gunpowder is probably a reasonable point to look at.