We can't explain it, but we do have some constraints: consciousness acts on the physical world and is definitely affected very directly by it. At some point it has to interact with the plain old boring Physics governing literally everything about our neurons and our bodies. And yeah, it's hard to explain how our puny brains can interact with this mysterious non-Standard-Model-Physics while particle accelerators, cosmic rays and neutron stars cannot.

Honestly, it just sounds like human exceptionalism and God of the gaps all over again. I find it pretty hard to justify "we don't know exactly therefore I can invoke magic". And not that I'm particularly skilled in philosophy, but AFAIK even Descartes wasn't able to go too far with dualism (which seems to be what you're arguing for).