Yeah it seems to me the entire process of cognition is based on fully material processes.

Not the process, the plane of existence where the object is. Many who have left Plato’s cave doubt that those objects are made of material.

If we take Plato’s cave to be the mind, and the projections upon the wall to be reality’s impressions upon our mind transformed into stimuli, then I don’t believe anyone could have ever left that cave anymore than anyone could have ever stepped their consciousness outside of their own brain to verify how well reality correlates to their mind’s interpretation of it.

Regardless, all this this conjecture is invariably happening within the boundaries of our minds, which seems to be composed entirely of physical phenomena.

Without a definition of what’s material in this context, this discussion makes very little sense.

We can’t see objective reality since all we see and sense have to go through our brains. What we can do is to interpret what we see and try to arrive at something that represents a consensus among our different perceptions.

Are you saying the mind is another form of interpretation? Where is that plane of interpretation happening?

We are only aware of the mind's internal representation of objective reality.

Who is aware? The atoms in the brain are aware?

Hard to draw a line without a good definition of awareness. An entire adult brain loaded with a life of experiences? Certainly yes. A 10-week fetus? Almost certainly no.

It is “the hard problem” :)