All the evidence we have is that somebody who wrote part of the New Testament says that the Holy Ghost was the father of Christ, and that somebody who wrote another part of the New Testament says that Joseph was the father of Christ.
Matthew and Luke give the genealogy and both show that Christ was the son of Joseph.
The "Incarnation" has to be believed without evidence. There is no way in which it can be established. It is beyond the reach and realm of reason. It defies observation and is independent of experience.
It is claimed not only that Christ was the Son of God, but that he was, and is, God.
Was he God before he was born? Was the body of Mary the dwelling place of God?
What evidence have we that Christ was God?
Somebody has said that Christ claimed that God was his father and that he and his father were one. We do not know who this somebody was and do not know from whom he received his information.
Somebody who was "inspired" has said that Christ was of the blood of David through his father Joseph.
This is all the evidence we have.
Can we believe that God, the creator of the Universe, learned the trade of a carpenter in Palestine, that he gathered a few disciples about him, and after teaching for about three years, suffered himself to be crucified by a few ignorant and pious Jews?