Someone asked me today--why the disciples didn't write about Jesus sooner, why they waited.  I replied, "They thought he was coming back immediately.  What was there to write about? 

He hadn't overthrown the Roman Government as the people had expected him to do--the Messiah was supposed to come and be King of the Jews of the lineage of David. That didn't happen the way they thought, but He would be coming back soon to reign.  Like, really soon--they thought.

Years later, Luke, a believer, but who had never met Jesus personally, became concerned that the apostles and Christians who had known Jesus were being killed, and their story would be lost. 

So he began to write to a friend, "Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us...as they delivered them unto us, who from the beginning were eyewitnesses and ministers of the word; It seemed good to me also, having had perfect understanding of all things from the very first, to write to you in order...that you might know the certainty of those things in which you have been instructed." In other words, "We have to record the eyewitness accounts.  We have to write this down."

He is the one who wrote the story about the birth, Magi, Herod killing Jewish baby boys, etc. that no one else did.  Luke had to have gotten that story from Jesus' mother.  He said he wanted to tell the story--in order--accurately, by talking to the people who were the closest to Jesus.  Luke got the story down for us to read and got it right.  The other Gospel writers emphasized other things.