Okay, while reflecting on the shortcomings of MoN, the chief one being that what happens in that game doesn't really seem like Nyarly's style, I had an idea. Since I'm a non-gamer I'll most likely never use it so I thought I'd post it here on the off chance that you can find a use for it.
Basically, some cultists are trying to bring their god's progeny into the world but due to a spectacular frak-up on their part they end up losing the mother. How they lose her is up to you, maybe she escapes, maybe the cult gets raided by the authorities for some reason and she gets rescued or taken into custody, but whatever happens she gives birth somewhere outside the cult's control, the baby seems normal enough to pass for human, and due to the circumstances is put up for adoption. A few years later, the cult, after a lot of scrabbling, finally manages to get a lead on where the child ended up and sets out to find them. The investigators could either be investigating what happened years ago and upon finding out what happened get into a race to find the child before the cultists do, or the child's adoptive family, who after one mysterious event too many set out to find the cause and promptly get pitched into the weirdness deep end.