1. As far as we know there is nothing non-physical in the brain (a soul or magical quantum microtubules or whatever). Everything that happens in your head obeys the laws of physics.
2. We definitely are conscious.
3. Therefore consciousness can arise from purely physical processes.
4. Any physical process can be computed. And biological thought appears as far as we can see to simply be an extraordinarily complex computation.
5. Therefore it is possible for a sufficiently fast & appropriately programmed computer to be conscious.
6. LLMs bear many resemblances to human thinking (even though they're obviously different in many ways too), and we've established that computers can be conscious, so you can't trivially rule out LLMs being conscious.
At least for now, I don't think anyone sane says today's LLMs are actually conscious. (Though consciousness is clearly a continuum... so maybe they're as conscious as a worm or whatever.)
The main point is that people trivially dismissing AI consciousness or saying "it can't think" because it's only matrix multiplications are definitely wrong.
It might not be conscious because consciousness requires more complexity, or maybe it requires some algorithmic differences (e.g. on-line learning). But it definitely isn't not-conscious just because it is maths or running on a computer or deterministic or ...