I agree with you that nobody can dispute a MAN named Jesus did exist, the contemporary historians mentioned him in their writings, e.g: Josephus Flavious, the Jewish historian.
By any measure the N.T passes every test for the accuracy of an ancient text. ANY MEASURE.
I believe that the Bible is maybe 90% accurate, however there are clear injections, e.g: twisting some verses to point to Jesus instead of God like the verses talking about God's coming in dense clouds along with the angels..etc
We have a final Proven testament, Quran, why don't you verify the physical incontrovertible evidence proving its authenticity?
Since God intended for it to confirm and supercede the Bible, it is equipped with this superhuman miracle. The original Bible may have a similar phenomena but due to the magnitude of injections, it cannot be restored, Quran on the other hand was restored to its original form after the miracle exposed only two false verses (intended to exalt Muhammad) in the text.