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The question is typically described as "the historicity of Jesus". https://en.wikipedia.org/wiki/Historicity_of_Jesus
There are similar debates for other famous ancient figures.
The general academic consensus on Jesus (and many similar figures) is that they did exist and many of the details have been fictionalized.
Conversely, there are many other people from his time that definitely did exist and verifiably so. I have a bronze coin minted in Judea by Pontius Pilatus. I can look at it, I can touch it, it's real. Even as an avowed agnostic, I see no reason why Jesus couldn't have been a real person (minus the miracles that were almost certainly later additions).
It figures that the source cited on the documents relating to his execution can only be read about in some guys book.