The system would not take any explicit stance regarding God or gods. And it wouldn’t categorically reject the existence of anything in particular.

It would merely have one guiding principle. Namely, it would decline to posit the existence of anything - unless there is democratically observable evidence for it.

So the default stance on everything - birds, bees, trees, humans, you, me, the sun, the moon, God or gods - is that they don’t exist.

Take air for instance - the transparent substance all around us. By default, we assume that it doesn’t exist. But if we can provide ample, publicly observable evidence (e.g. leaves scattering in the wind, chest and belly expanding when we breathe), then we can be comfortable positing its existence. And we would then consider our initial assumption (of nonexistence) disproven.

Does that make sense? We assume nonexistence, and then try to disprove that assumption with evidence.

The same would go for gods. By default, we assume their nonexistence. But, if there is democratically observable evidence for a god, then we can be comfortable positing their existence, and rejecting our initial assumption (of nonexistence).