It's 'may God' not 'may a god'

You can't compare the word "God" with "Bog".
The word "god", for almost the entire history of the word in this general form, has been used to refer specifically to the god of the Jews.
On the other hand, the word 'bog' has been used in this way for but a thousand or so years.

So this saying came into being upon Christianity reaching our ancestors? I think not.
That's the only way it could have anything to do with Christianity.

Otherwise, it's talking about one of many gods, most likely Dajbog.

The form, 'bog', is indeed talking about one god, and I've read over and over again that Dajbog was the 'supreme' god of the Serbs.
It is then, very different, and makes more sense.