I don't believe it is out of the realm of possibility .. and is it not the Biblical way things are done ? .. Mary gets a visitation by one of those demi-gods "Angels" if that is the term you prefer .. who came to know Mary .. who delivered the seed .. so to speak.
Jesus is fully man .. and knows not his Father according to Mark's gospel .. nor is Jesus well aquainted with "The Father" - presumably does not know of his half man/half god status until he meets with John the Baptist as a man of 30.
Only then does the Most High God reveal to us that he will adopt Jesus as his Son .. The Son of Man .. in the physical sense .. Son of God in sense of one being adopted by God.
Even after the Christening .. we do not know if Jesus is yet divine .. first he must go through the ritual trial .. pass a few tests.. like the Pharonic King making ritual .. only after you pass through the test/ritual do you get the half man /half God Status.
Then in that Ritual .. we meet one of these "Sons of God" .. of similar or greater stature to the ones we met in Genesis .. and in Job.
and who is this God who is sent to Test Jesus ? Pleased to meet you .. our Good friend the Tester .. one of the Son's of God mentioned in Job .. an entity with some serious God- powers .. including not just hurling thunderbolts .. but power over the entire earth.
This demi-God .. sent by the Most High God .. to test our Lord and Savior. Jesus passes the test .. survives .. and goes on to perform many works of wonder .. like the hero's of Old .. offspring of human and God .. told to us in Genesis.. 6 NIV
When human beings began to increase in number on the earth and daughters were born to them, 2 the sons of God saw that the daughters of humans were beautiful, and they married any of them they chose.
So you see .. these Sons of God took many a human Bride .. the offspring of which were the
"heroes of old, men of renown"
4 The Nephilim were on the earth in those days—and also afterward—when the sons of God went to the daughters of humans and had children by them. They were the heroes of old, men of renown.
So why would Jesus not be conceived in the same way .. offspring of one of the Sons of God -- and a human .. Mary in this case. Why would it be any different ? Jesus too became a hero .. a wonder worker .. a man of renown.. having divine powers above that of a normal human... but unfortunately not strong enough to save himself from that horrible fate at the hands of the Romans and his fellow Jews.