[Solon]

I'm in.

It's a fairly common explanation in the ancient world for men who won great acclaim. Sex between mortals and deities happens all the time in Greco-Roman myth (which is highly derived from ANE myth).

Some examples of mixed-parentage characters from myth:

Herakles / Hercules
Theseus
Perseus
Sarpedon
Achilles
Aneas
Helen

Some of these half-human / half-god people even achieved deified status:

Dionysus
Polydeuces (although he willingly shared it with his twin Castor)
Herakles

Some historical mortals were so famous that their genealogies were revised to make them the sons of gods:

Alexander the Great
Theagenes of Thasos
Euthymos of Locri


As in so many other ways, the Jesus story fits in nicely with its mythic parallels. In none of these (other) stories, however, does anyone pretend that the mother remained a virgin.