I never said the main or the only problem is that four decades separates the earliest gospel from Jesus's death. I just raised that fact to test your knowledge of history. There are a gazillion problems with the historical reliability of the New Testament. You don't even have to go further than Wikipedia to get the gist of it:

'Historians subject the gospels to critical analysis, attempting to differentiate, rather than authenticate, reliable information from possible inventions, exaggerations, and alterations. Scholars use textual criticism to resolve questions arising from textual variations among the numerous manuscripts that have been discovered to decide the most reliable wording of a text as close to what the "original" may have looked like. Scholars seek to answer questions of authorship, date and purpose of composition, and look at internal and external sources to determine the degree of reliability of the gospel traditions...

'The scholarly consensus is that they [the canonical gospels] are the work of unknown Christians and were composed c.68-110 AD. The majority of New Testament scholars agree that the Gospels do not contain eyewitness accounts; but that they present the theologies of their communities rather than the testimony of eyewitnesses.'

https://en.wikipedia.org/wiki/Historical_reliability_of_the_Gospels