Fact is, there was so little time between the events recorded by the New Testament's authors and the time that the authors set their accounts of those events down on paper that there was no opportunity for the full-blown mythologizing process the New Testament's detractors suggest.
In comparison to the events recorded in other ancient texts, the New Testament is the ancient world's equivalent of the text that just flashed across your cell. The same is true of the earliest known texts of documents attributed to far earlier authorship.
As you can see from the chart below, everything about Jesus was documented closer to the events recorded and more extensively reported than is true of documentation about other figures in the ancient world or the literature it's believed those figures produced.
There is more reason to believe the accuracy of the New Testament's accounts of Jesus' life, death, and resurrection than there is to accept other ancient documents' unquestioned accounts of Socrates, Aristotle, or Julius Caesar.
[Click to enlarge.]