This is more of an anthropological question more than a historical question. All the same, it has been noted by many sources that facial expressions and basic sounds (huh?, mama, etc.) are fairly consistent over nearly all of the cultures around the world now. I even remember reading an article recently that went over how speakers of Russian even said Huh in conversation even though the Russian language has no H sound. Based on the similarities there, and descriptions of laughing in older texts (The Oddesy is the first that comes to mind) we could generally conclude that any random culture picked from any time in the history of Homo Sapiens has a high likelyhood of sharing a similar sound when laughing, with added slight differences from accents of course.

Well, according to Mary Beard (Laughter In Ancient Rome) they transcribed the sound of laughter as "Ha-ha", which is where we get our transcription of the sound.

Certainly a great many of the things they laughed at are very similar to sort of thing we laugh at today. For example, I have a collection of Roman jokes round here somewhere and it reads like something from the 70's.