Well there is a movie that's along these lines.
Agnes of God
Any number of plausible explanations.
If both people are truly mystified, do a fetal blood sampling (Chorionic villus sampling or
CVS). Results can be obtained 13-15 wks after last period of the female.
If the DNA typing shows 'god' to be of a common Earthly ancestry, then you can go from there.
We have lots of DNA markers which are related to traits, or disease markers, or even ability to taste or smell certain chemicals.
Now if the Karyotype shows that the 'father' had, oh, some really odd number of chromosomes, then reason to suspect something paranormal. (some
mutations have an extra chromosome)
Spectral karyogram of a human female (Wiki)