John, the last Gospel written, says nothing about Jesus birth, and neither does Mark. Since John thought that Jesus’ divinity was eternal, a birth story illustrating where that divinity came from was not necessary. The two gospels with the birth narrative could indicate that it was at Jesus’ birth that he became divine. Also, early manuscripts of Luke (I believe) had the proclamation of God read as: “Today I have begotten you”, which indicates that Jesus became the Son of God at His baptism by John. Finally, Mark shows Jesus as very human, suffering and emotional, right up to the moment of His death. This could indicate that Mark believed that Jesus became the Son of God at that moment, or even at his Resurrection. Again, if that is the case, there is no reason to have the miracle birth narrative, which is not in Mark.
So you have various possibilities. Depending on which Gospel you look at and how you read them, Jesus became divine:
When He was born,
When He was baptized,
When He died,
When He was resurrected,
or Always.
This was a big issue in the early church, and it took a couple of hundred years and several councils (and declarations of heresy) to sort it all out. The Church went with Big John regarding this, but it was not universally agreed upon for some time. The Gospels are not very clear about it; read them for yourself.