Luke 1:1-4 KJV
1 Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us,
2 Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word;
3 It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus,
4 That thou mightest know the certainty of those things, wherein thou hast been instructed.

Call of the historian Theophilus to write down what was believed among the ones that followed Christ. A historical documentation for others to have this account of what was believed and had been witnessed among the believers.
The story in Luke and Matthew(Peter's account) of the Messiah birth was information needed to provide not historical account but information use when studying prophesy of the Old Testament for accuracy that Jesus is the Messiah. Without this physical writen evidence, we can only rely on the Holy Spirit to testify to the heart of the unbeliever that Jesus Christ is Lord.
A good example of the Holy Spirit comes with Saul/Paul own testimony on the road to Damacus.The testimony of Christ cross in the story of Cornelius, and perhaps even more would be the story Ethiopian Eunuch as well as the jailor that set Paul and Silas free. The origin of the virgin birth important to share along wirh the forerunner of Jesus story more know as John the Baptist mysterious birth through prophesy to a family of old age like founding father of the Jewish faith Abraham and Sarah promised birth of Isaac. John the Baptist parents being Zachariah and Elizabeth. They follow a God that spoke revelations of prophesy not only to their heart but their physical and mental eyes. The four Gospel account of these two men recorded for a testimony if both humanity and filling and anointing as the chosen to do the work of the Messiah.
Dear Heavenly Father thank you for the evidence left behind of both the forerunner and the Messiah, in Jesus precious name, Amen.

Continual Scripture Study: Acts 10:34-43 KJV
34 Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons:
35 But in every nation he that feareth him, and worketh righteousness, is accepted with him.
36 The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all:)
37 That word, I say, ye know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached;
38 How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing all that were oppressed of the devil; for God was with him.
39 And we are witnesses of all things which he did both in the land of the Jews, and in Jerusalem; whom they slew and hanged on a tree:
40 Him God raised up the third day, and shewed him openly;
41 Not to all the people, but unto witnesses chosen before of God, even to us, who did eat and drink with him after he rose from the dead.
42 And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead.
43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.