There is definitely very vulgar Roman graffiti preserved in the ruins of Pompeii. Particularly comments about homosexuality, and sexual conquests, and generic insults, and generic "hellos".

Considering the casual nature in which these works were done, and the the sheer number, there is no doubt they are far older than the destruction of Pomeii in 79 CE. It's a matter of finding stuff like this preserved. Graffiti tends to be, by its very nature, hastily done and not with longevity in mind. A writing done on a wall with charcoal is not supposed to outlast the wall.

My personal favorite from Pompeii: "Celadus makes the girls moan!"

Stage directions are not preserved in the Classical text, but it is highly unlikely that the rural Dionysia scene and accompanying song to Phales in Aristophanes' Acharnians was played straight. ("Sauce the cake" indeed.)

And if that doesn't count, there's all sorts of genital puns going on with the Megarian and his daughters and at least one more at the end. If none of those count for whatever reason, the rest of the Aristophanic corpus - the ones that spring to memory are those in Clouds and Lysistrata has them as well. Yes, more fart and shit jokes than dick jokes, but dick jokes, too.

That takes us to 425BCE at least, and, based on how there doesn't seem to be anything unusual about the jokes in the comic context, earlier still, and it would surprise me if someone couldn't find earlier ones.