How do we determine, via historical methods, whether someone existed or not?
Most of us common people will be lost to history. Well… maybe not, with the Internet and blogs possibly lasting into perpetuity (but even a blog could be used to create a mythical person). But for pre-Information Age peoples, they will almost all be lost to history. Unless their existence is inexorably tied to some sort of historical event. An event that leaves its mark on history: like the Civil Rights Movement, WWII, the Greco-Persian wars, the Romance of the Three Kingdoms, and many other brute-fact events that shape the world. There are people who have defining roles in these events that necessitate their existence.
How could we tell a coherent story about the Civil Rights Movement without MLK? Or the conclusion of the Greco-Persian wars without Alexander the Great? World War II without Hitler?
Someone like Moses, his identity is inexorably tied to the Exodus event. Since there’s no evidence for the Exodus (and actually evidence diametrically opposed to the Exodus story), this more than likely means that the Exodus didn’t happen. If there was no Exodus then there’s no person that we could identify in history as “Moses”.
It would be like saying Moses’ defining role was that of the president of Atlantis. Since no Atlantis exists, it effectively means that this “Moses” character said to be the president of Atlantis similarly didn’t exist. Sure, there could be a person who really lived but had claims of him being the president of Atlantis thrust on him (or he himself claimed) but historically we would not be able to call this person “Moses”. This is because the historical Moses can only be defined by his intimate connection to a historical event or person.
Jesus, on the other hand, has the opposite problem. There were probably thousands of Jews crucified in the 1st century, and many thousands more had the name “Jesus” (that name is the Latinized Greek form of the Aramaic name Joshua). So it would be impossible to identify one of these Jews as THE Jesus.
You would need a bit more historically identifiable material to locate, historically, the Jesus depicted in Christian myth. What is the defining role of Jesus? The one specific role that separates this Jesus from the possibly hundreds of other Joshuas crucified in the 1st century is his resurrection. But this is a supernatural event so it’s impossible to locate in history.
Other than that, there are sayings attributed to Jesus but this has problems due to them appearing relatively late in the Christian timeline. Whenever Mark was written is the earliest that the teachings attributed to Jesus appear. But then we have to figure out when Mark was written and then do some sort of literary analysis on the text to determine its genre (i.e. how it is intended to be read and understood). Are they really the sayings of Jesus, or are they the sayings of Mark? What makes them more likely to be the sayings of Mark is that they first appear in Mark. No Christian writing prior to Mark seem to be aware of any sayings of Jesus, and we have no contemporaneous writings from anyone who personally saw Jesus preach (or even saw Jesus crucified).
If one were to posit that the historical Jesus is possible to find, they need to come up with some sort of “checklist” that one would need to fit the Jesus that started Christianity. What is the threshhold for historicity? A Jesus that preached but wasn’t crucified? A Jesus that was crucified but didn’t preach? I really don’t know.
So really, Moses more than likely didn’t exist due to the Exodus being fiction. Jesus, on the other hand, is impossible to identify in history because there are too many of him; the historical criteria for finding Jesus are too vague and nonspecific.