If it were possible for a woman to impregnate herself, she would have to produce sperm as well as an egg. She would not be a woman, she would be a hermaphrodite. If a woman did somehow enable the development of an egg without sperm, it would not have a Y chromosome. The child would be a female, not a male. If the child did have a Y chromosome, the mother would not be a woman. She might look like a woman, since XY foetuses can develop into the default female if the Y does not become active at the right time, but she would not be a woman. That being so, she would probably not have a womb, or the ability to make eggs. There would be no child. If Jesus did not have a father, then he was the result of some miracle.
If girls were married at 13 in first century Palestine, it would be unlikely for them to fall pregnant at once. The onset of menarche has been falling recently - and the average age would have been higher than 13 where food was less abundant, and less rich in oestrogen mimicking compounds than it is is modern western societies. There is a greater chance of miscarriage and of maternal death with young mothers, whose pelvis is undeveloped. The mother is less capable of caring for the child. Would God be involved in using an unfit and risky vessel, however pure, to the possible detriment of his offspring or the baby's mother? (Would an alien, who had presumably been watching the way humans develop?) I think not.