What's the experience (Gr. empeiria) of our (self)consciousness? In self-reflection, "a finite container of mental images" sounds plausible hypothesis to start from, some sort of space-time sheet filled with mental images (various sensations and linguistic thoughts). And from cognitive science we know that this space-time sheet has at least the aspect of electro-magnetic field that can be measured (EEG) and correlates with various mental states.
By "God" we usually mean, at least, something bigger than us. So hypothesizing god(s), a natural suggestion would be that it is scaled up level(s) on conscious experience, inside which "we" etc. of included size scales are mental images, "Gods thoughts". A "
Russian doll" continuum of scales of consciousness would be next natural hypothesis, each level would be finite container of mental images, but the continuum of scales could be infinite.
In this hypothesis godhood would be relation of inclusive scale to it's contained mental images, e.g. from perspective of single cell in human organism the organism would be it's god. And the whole infinity of size scales could be defined as the God with capital Gee.