Yes, we do have fourth century manuscripts, but that’s only evidence of ancient non-eyewitness second-, third-, fourth-hand hearsay testimony, as written down by authors who were not themselves eyewitnesses. So this is irrelevant objective evidence which does not directly support a miracle claim, precisely because it’s irrelevant. Believers will also point to objective evidence such as the archaeological findings of the Pool of Siloam in Jerusalem, where Jesus supposedly told a blind man to go to be healed and was healed. But findings like these are not considered relevant objective evidence.
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