My understanding is that the gospels were written several hundred years A.D.
This is plainly erroneous. We have manuscripts of the New Testament dating from within the first century AD. Seeing as Jesus died around 30 AD it is very early accounts.
Josephus the first century Jewish historian says about Jesus the following
Flavius Josephus (AD 37?-101?) mentions Jesus - Antiquities, Book 18, ch. 3, par. 3.
Now there was about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Gentiles. He was [the] Christ. And when Pilate, at the suggestion of the principal men amongst us, had condemned him to the cross, (9) those that loved him at the first did not forsake him; for he appeared to them alive again the third day; (10) as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians, so named from him, are not extinct at this day.
You can find the full accounts of 1st century historians attesting to Jesus in the following link
It is also curious to note that if you take away the extant manuscript of the New Testament then you can still deduce the content of the bible from the early church correspondence.
One church would write to another and quote a bible verse and warn the other church about possible heresies. This gives us another early sources to compare manuscripts with to deduce the authenticity of the message
If you are interested in a more intense account of these matter I should recommend to you the book "Evidence that demands a verdict." By Josh McDowell. Really a excellent resource for anyone who wants to know the truth about these matters.