Sumerian jokes? Well, hard to find any original ones (and the one above, obviously, is not).
There has been a claim that something written in Sumerian on a tablet from 1900 years BC. It says " "Something which has never occurred since time immemorial; a young woman did not fart in her husband's lap." Does that sound like a joke to you? Well, maybe. But note two things: the first is that I have seen many cases of Sumerian texts translated in completely different ways by different experts. So, maybe the translation for this one is good, but I wouldn't bet on that. The second is that we have plenty of Sumerian texts surviving. Even if you didn't spend some of your time examining them, you ought to be surprised that, out of so much material, only one joke came out (if it is one). Indeed, Sumeria left us a vast corpus of hymns, narrations, and stories. Most rather solemn and serious, the sense of humor, in those times, was not the same as it is in ours.
A little better is an Egyptian text from some 1600 years ago, said to be about Pharaoh Sneferu (from the same source as above). "how do you entertain a bored pharaoh? You sail a boatload of young women dressed only in fishing nets down the Nile and urge the pharaoh to go catch a fish." A joke? Maybe. Still, not the kind of joke that makes you go ROTFLMAO.
Instead, the Romans had a jokes similar to ours. One is from the Saturnalia by Macrobius, around 4th century AD, as reported in Wikipedia.
Some provincial man has come to Rome and walking on the streets was drawing everyone's attention, being a real double of the emperor Augustus. The emperor, having brought him to the palace, looks at him and then asks: "Tell me, young man, did your mother come to Rome anytime?" The reply was: "She never did. But my father frequently was here."Again, no ROTFLMAO involved, but we are getting a step closer to modern jokes. In our times, when thinking of a Roman joke, we could say something like "A Roman walks into a bar and asks for a Martinus. You mean a Martini, the Bartender asks. The answer is, if I had wanted it double, I would have asked for it." Different kind of stuff, I'd say.
So, the records of ancient jokes are poor, but there seems to have been a slow evolution toward our times. "Jokes" are one of those slow trends that go on for millennia. And I think that jokes have a purpose: they have evolved with the increasing complexity of society. They serve as a tool against the psychopaths who tend to infest governments and rule states.
In the early times, states were still something new, so it took centuries for jokes to be developed. Now they are a powerful weapon against dictators, pompous rulers, and bureaucrats. In many cases, rulers reacted violently: in some places and some times, telling a joke about the local big man could you get you jailed or worse. Fortunately, today things are different. By the way, do you know the joke about Donald Trump......? Hmmmm........ Well, now that I think about that, I see that don't know any, actually.