The Begetting of the Son in the Virgin
It’s explicit in Luke 1:35 that the Virgin conceives by the Holy Spirit that is why her offspring will be called “God’s Son”.
There was no human father involved. It’s just the Holy Spirit and the Virgin as recorded in the Bible:
“She [Mary, the Virgin] was found to be with child through the Holy Spirit” (Matthew 1:18 NIV)
Hence, Gabriel is right when he proclaimed that the Holy offspring to be begotten in Mary will be called “God’s Son” because the one she conceives is the pre-existent offspring of the Father without human father just as John also firmly believes ( John 1:1-18).
Matthew concurs with Luke, the one begotten in the Virgin is “the God [who is] with us” (Matthew 1:23).
The begetting of God’s own Son in the Virgin through the Holy Spirit is a messianic prophecy (Isaiah 7:14).
Again, the reason why the one to be begotten in the Virgin will be called “God’s Son” is because of lack of human father to be involved because it is already having a Father who is God himself.
Gabriel believes that the one the Virgin conceives is without a human father but is conceived only through the Holy Spirit and that the one the Virgin conceives is God’s own pre-existent Son that is why the offspring will be called “ God’s Son” not “Joseph’s son” as soon as it was conceived.
The Son of God was named Jesus just as expected. The one the Virgin conceives and gives birth to is a one person with two unmixed, united and distinct natures: divine and human as the Chalcedonian Creed affirms.