Nobody knows how. But the fact that there's nothing else but fully known and understood physical forces pushing around the particles that make up my brain is rock solid science.
You're claiming that there's nothing but physical forces at work because we've yet to observe anything else. axguscbklp is claiming that subjective experience is such an observation.
To find out which position is correct we must attempt to find a link between physical phenomena and subjective experience. If we are not able to find such a link then perhaps they are not actually connected after all.
You are assuming such a link exists and has just not yet been scientifically articulated. For what it's worth, from my own review of the literature, I tend to agree we have been making progress on this front and will likely find a link eventually.
Consciousness could simply be an emergent phenomenon. Mathematical theorems and proofs are not physical things, yet we can create physical systems that can encode and prove theorems. Maybe we are conscious in the same way that these physical systems prove things without being made of mathematics.