Sorry to jump in late.
How about this for a theory/possibility?:
God had a plan for Mary. Her parents prayed to God for a blessed child, and one that they would devote to God. In Jewish culture, as I understand, it is only males who can be dedicated to the service of God. God did hear their prayers and informed them that the child would be so blessed. They were surprised that a girl was born, but God reassured them that she was special.
When the time came, Mary gave birth without the intervention of a male partner.
This is a miracle.
Now, what a theory may be is that Mary was born with the facility to have a child without the agency of a man. She naturally could carry a child via a process of parthenogenesis - or some other name - where she actually had within her the ability to produce and fertilise an egg, and form an embryo.
God had this as His plan, and she was born with this facility. Rare, and in this case it is a miracle - but one within the realms of scientific possibility.
It was therefore a virgin birth, of a man with manly characteristics - all man and in no part God. (God doesn't have DNA as He is not made of matter)
Does this tackle the thorny issue in the OP? Any flaws to the theory (other than it would be so rare an occurence it could be termed a 'miracle'?)
Cheers,
Shafique