Usually when people ask that question or make the statement that Jesus either did or didn't exist they mean the "Biblical Jesus" as he is described in the New Testament. Once you stray from that question you have an infinite variety of possible Jesus' and possible answers to the question. As a result I think it is impossible to "put it to bed" so to speak. If you confine your question to the "Biblical Jesus" all atheists agree, THAT Jesus did not exist.
Did some person who resembled the Jesus in the New Testament without all the supernatural claims exist? It depends on how and in what way he resembled the Biblical Jesus even without the supernatural elements.
However, the only real question that is really important for nontheism as it confronts conservative, evangelical, fundamentalist Christianity is about the Biblical Jesus.
Not only does there appear to be no historical evidence for Jesus of Nazareth (who is really who people are talking about), there is a good chance there was never a Nazareth.
Try this site: Jesusneverexisted.com
You can ask the same of any alleged historical figure. The same requirements for evidence would need to be applied. The problem is that the historical evidence for Jesus is woefully paltry by comparison with other historical figures and events.
What's more when people say, "Do you think Jesus existed" you have to ask, "which Jesus". If you mean the one portrayed in the gospels, well then you have to deal with all sorts of claims to the supernatural. These are not simply claims on a par with other historical events like Caesar crossing the Rubicon or Herod being the governor of Judea or even Herod killing all the children under two years of age. Those are "normal" events the "sort" of which occur regularly throughout history.
The problem with Jesus is that whether he existed matters. For example, if someone were to come along and say Shakespeare was not a real person, as some do then there is lively scholarly debate, but at the end of the day, it doesn't matter. Someone wrote the play, perhaps multiple someones and they stand on their own. With Jesus it's different.
Traditional Christianity is based on the actual historicity of the Jesus of the gospels who did and said everything attributed to him. Without the actual Virgin Birth (not mythological, not metaphorical, not symbolic), without the actual atoning death and resurrection, there is no Christianity. What's more those things had to be done by the Jesus who was the God-man. So it matters.
Bart Ehrman has a rant on what would be required by historian to prove or at least determine as highly probably, the occurrence of an event or the existence of a person and NONE of them apply to Jesus. The fact is that you cannot PROVE anything that occurred in the past, you can only argue for it's probability based on the extent and nature of your evidence.
In my opinion a person by the name of Jesus who did and said some of the thing attributed to the Biblical Jesus may have existed but it is impossible to be sure and it really doesn't much matter.
"You can ask the same of any alleged historical figure. The same requirements for evidence would need to be applied. The problem is that the historical evidence for Jesus is woefully paltry by comparison with other historical figures and events."
Your two first sentences are very rational, but your assertion in the last sentence doesn't really stand up to closer investigation. It's true that we should compare the evidence we have for Jesus with the evidence for other similar figures in his timeframe (obviously if we start comparing the evidence for Jesus to that of Caesar than it will look paltry; one was one of the most influential people that ever lived and the other was most likely a charismatic preacher at best).
We need to compare the evidence we have for Jesus to the evidence we have for other Jewish preachers, like Theudas, like Hillel, like the Samaritan Prophet, like the Egyptian Prophet, etcetera. And when we do that, we find that the evidence for Jesus is on par (and even slightly better) than what we have for these figures.
"Bart Ehrman has a rant on what would be required by historian to prove or at least determine as highly probably, the occurrence of an event or the existence of a person and NONE of them apply to Jesus. The fact is that you cannot PROVE anything that occurred in the past, you can only argue for it's probability based on the extent and nature of your evidence."
Bart Ehrman has pretty much made a career out of providing evidence that the Jesus of the Bible was most likely an apocalyptic preacher (as he does in his book "Jesus: Apocalyptic Prophet of the New Millenium"), so clearly he does think that there are quite some things who can say about Jesus with a rather high degree of probability.
There is little doubt in Ehrman's mind that Jesus has existed; that's why he's able to write books about not even that he merely existed, but even about what kind of person he probably was.
Nevertheless it's true to say that we can only ever provide evidence for historical claims, we can never "prove" them (in fact, according to many definitions, being able to "prove" something is limited to mathematics). We can only talk about events that have been established to have occurred with a high degree of probability.
Jesus as a historical figure is in that category.