> is this a falsifiable claim?
Yes, we can observe animals at various stages of consciousness and correlate their brain structures (or lack thereof) with consciousness tests (such as the mirror test).
Assuming consciousness isn't primarily a function of brain structures, we'd expect to find animals, plants, or bacteria that defy our predictions of consciousness.
> Is there any proof of this?
Yes. Beyond being able to observe varying levels of consciousness in animals, we've seen the impacts of traumatic head injuries to people. Their entire personalities change, they sometimes become unconscious (think vegetative state). We are fairly confident when operating on brains which parts control what. And we have interesting diseases like split brain syndrome where 2 separate consciousness develop in individuals when there is damage to the bridge between the brain lobes.
> Until we can replicate consciousness (heck, until we can even measure consciousness), this is as much a matter of faith as any other belief about how consciousness emerges.
This is a bit of a leap. With many physical sciences, we don't need to replicate things to make predictions, observations, and conclusions. We don't, for example, need to replicate a supernova to understand how stars are formed.
> But I've yet to see anything come close to explaining the phenomenon in a testable and falsifiable way, placing this entire subject outside of the realm of rational science in the meantime.
Have you looked and are you a biologist?
Look, I'm not a biologist, just someone interested in the subject. But from my own personal research on what it known, it's far less a mystery than what you might assume. For example, modern biology doesn't really recognize consciousness as being just a binary on or off sort of thing. There are multiple parts to it that all function in tandem.
The unfortunate thing is that consciousness is not simple. Because of that, it's not something that you could reasonably expect an explanation of in a comment. But if you are interested in a primer then this looks to be a good article [1]
[1] https://thereader.mitpress.mit.edu/how-did-consciousness-evo...