What is that composed of? I would say thoughts, feelings (somatic, sensory, psychological, psycho-motor state) and memories. Ok so - now supposedly fundamental atomic "consciousness" is actually composed of reducible parts. At least three, thoughts, feelings, memories. Which of these is scientifically unexplainable in principle? Thoughts are models of something, like an equation, image, or a program. Feelings are the product of sensory-thought integration. Memories are simulations of past thoughts and feelings. I think subjectivity is an illusion. Probably in a minority here though.
With a sufficiently powerful scanning tool i.e. super fMRI you could measure the neurocorrelates of thoughts and feelings.
Consciousness is a word. Subjectivity is an illusion existing in living people. Obviously past historical figures are not subjectively conscious because they are dead. So where did this supposedly existing thing "consciouness" go? Wouldn't a simpler, more scientific explanation be that it never existed to begin with. You say denying consciousness as a real extant thing is akin to religious belief but then you agree there is no possible mechanism for how it could arise materialistically. Isn't it simpler just to say it doesn't exist as something separate from the ensemble of functions of a living brain after all?