Oh, I thought CE started exactly at crucifixion but I guess that wouldn't really be possible if people didn't know when it really was. So it's accepted that those 3 authors may have personally seen Jesus and followed him around collecting stories?
Lee Strobel has a good take on the authenticity of the Gospel account in his book The Case For Christ [0] and as always the book is better than the movie
[0] https://www.goodreads.com/book/show/73186.The_Case_for_Chris...