I mean, if you accept the assumption that consciousness is biological (so there is no soul or other spiritual or metaphysical entity), then there is some algorithm or processing model that produces genuine consciousness: The one that takes place in our brains. The question remains if this processing model would be in any way similar to the processing model that LLMs use - and yes, we can probably rule that out pretty…
You're making an assumption out of thin air here: that consciousness is somehow produced or emergent, or that if it isn't you're in the realm of spiritual or something. What's your basis for that assumption other than just asserting it?
Yeah, I genuinely only see those two possibilities: Either consciousness is somehow the result of the interactions of (some of) the billions of neurons in our brain - or it isn't. If it isn't, either consciousness is a product of some other biological or physical* process that so far isn't identified - or it isn't. And if it's not the result of any physical process then I don't see what would be left except metaphysics.
We don't know as of now what consciousness is or how it is produced - but I think there are some strong hints that in fact it is produced by the interactions of our neurons. Mainly that we can directly influence consciousness with psychoactive drugs - which don't do anything interesting physics-wise except affecting how neurons exchange signals - and that we can also observe certain patterns of physical activity in the brain using EEG, MRI and other technologies and map this activity to mental tasks like concentrating or relaxing.
Edit: * I used "psychological" there but that was a typo. I meant "physical".