How do the gods become corporeal in American Gods?

Question

In American Gods, Gaiman appears to have been deliberately vague about how the gods come into corporeal form in their new homeland of America. The only reference I came across is to the dead Mr. Wednesday stating to take shape again in the mists of a cave or something, as a result of Shadow's efforts in passing through the underworld. Then Shadow realizes the truth about his plot with Low-Key and abandons him, and he vanishes back into the mists. I think. I'm probably muddling plot points.

Even in Shadow's discussion with Hinzelmann in the Epilogue, Hinzelmann mentions how he came to America "in the mind of a German immigrant", and a description of how belief in him started east of the Rhine 2,000 years earlier, but I'm still confused as to how he manifested even in his land of origin.

Just to be clear, I'm wondering whether the actual process of manifesting is actually referred to, or was it left up to our imaginations that they sort of 'emerge' into physical bodies, e.g. did Hinzelmann emerge into a solid form as an old man 150 years ago? Or was he born and grew up? Shadow is the son of Wednesday, so HE was born, and appears to develop some mildly godlike powers by the end of the novel (scrubbing people's memories).

Answer 1

There's a few mentions of the Gods coming over with the settlers and immigrants from various 'Old World' countries, the clear implication being that they're pale "incarnations" of the original deities.

Wednesday speaks to their origins;

When the people came to America they brought us with them. They brought me, and Loki and Thor, Anansi and the Lion-God, Leprechauns and Kobolds and Banshees, Kubera and Frau Holle and Ashtaroth, and they brought you. We rode here in their minds, and we took root. We traveled with the settlers to the new lands across the ocean.

Corporeality (and indeed immortality) seems to be something that the Gods have thrust upon them at the time of their creation. They can be substantially diminished through lack of belief but they cannot not killed by conventional means, tending to simply persist anonymously.

"Would you believe that all the gods that people have ever imagined are still with us today?"

The clear implication being that raw belief is sufficient to provoke their inception.

There's a moment where we see Wednesday switch between his discarnate and incarnate forms...

"There was a change in the shadows at the back of the cave. Something became more solid; something shifted. "You know too damned much, m'boy," said Wednesday's familiar rumble."

...but there's no reason to think that this isn't simply set-dressing intended to awe the still-naive Shadow.