[Emma_Goldman]

What do you mean it's 'too big of a thing' to be explicable within the framework of the physical universe? That does not sound like a sensible intuition to fix on. For most of history life was thought of as too big of a thing to be explicable in terms of the physical universe, and philosophers appealed to the divine and extra-physical vitalism, but we now know that life really is susceptible to physical explanation.

As for your question as to why humans or other sentient beings would be conscious if they belonged to the physical universe, the answer is obvious: for the same reason that we and other animals possess all other attributes, because of its functional value in enhancing our survival fitness as a species. Perhaps high level information-processing requires consciousness, or consciousness is a byproduct of some or all high level information-processing with organic matter.

I should say I'm agnostic about consciousness because I think we know next to nothing about it.