This is one interpretation of the story, but definitely not the accepted interpretation amongst the varying sects of Christianity.
Catholicism espouses that Mary was without sin, and Protestants generally disagree (Lutherans being the notable exception). They also believe that the trinity is intertwined yet separate (God is the father, Jesus the son, and the spirit a procession of both)
Most protestant sects generally believe that Mary was not without sin, but did indeed become pregnant without sex. They consider Jesus the biological son of God, and therefore fully human and fully divine (this is supposed to be a paradox and not make sense). Jesus is affirmed to be God’s actual son in all 4 gospels and several of the Epistles.
There doesn’t need to be a “logical” explanation free of contradictions and impossibilities in Jesus’s origin, simply due to the fact that he is God, and therefore above human understanding.
Source: I grew up in the church and was surrounded by theologians against my will. I got out, but the knowledge is still knocking around in my head.
