The Caesar-Jesus claims, about similar evidence for their existence, are more like a kind of folklore/gossip and they take many forms. One of the variations is that there is the same evidence for Caesar crossing the Rubicon as there is for Jesus rising from the dead. It's good to be skeptical of claims like that. The hole left by removing Caesar from physical history is gigantic, while removing Jesus from physical history leaves basically no hole at all- there absolutely had to have been a Caesar, but there did not have to be a Jesus. We have many contemporary accounts of Julius Caesar, and zero of Jesus. I'll even apologize for that by saying that we shouldn't expect there to be much evidence of Jesus.
Thank you for presupposing the laws of physics and not bothering with the magical stuff, I really do appreciate that kind of honesty, because it exposes your views to verifiable claims.
If I had to bet the house, I'd bet it on Jesus not existing, but I wouldn't want to make that bet. This is where I ask: "If no miracles, then what Jesus are we left with?" And that's a very important question, because the answer to it greatly affects the probability of his existence. If we're left with a Jesus who went around stirring up a little trouble and was executed in a small group lost to history, and later revived in religion by a cultist, then it's not crazy at all to believe that happened. But if we're talking about whip-the-temple Jesus and a roaring crowd of Jews calling for his head, and Pilate breaking character, well, that is not nearly as believable or likely.
What is the minimum historical Jesus that counts as "Jesus?" I really don't see that bar being cleared by Josephus, for instance.
For me, the best argument from evidence is that we know Pilate existed, in exactly the right time and place. Not only do we have the scriptural and early historical references, but we also have the best physical evidence we could hope for, found in Israel in modern times ("Pilate Stone"). I assume it's not a clever fake. Since we have Pilate, and scripture got him right, that helps the chances (a little, not a lot) that a Jesus was executed under his authority.
My bet for the "prehistoric" rise of Christianity is cultism and astrology, especially as a response to mysteries (and depicting the turning of the age), and apocryphal stories that coalesced in a mixture of truth and myth. In other words, I think our Jesus is dissolved in the soup.