So any other Turing-complete model can emulate it, including a computer. We can even randomly generate Turing machines, as they are just data. Now imagine we are extremely lucky and happen to end up with a super-intelligent program which through the mediums it can communicate (it could be simply text-based but a 2D video with audio is no different for my perspective) can't be differentiated from a human being.
Would you consider it sentient?
Now replace the random generation with, say, a back propagation algorithm. If it's sufficiently large, don't you think it's indifferent from the former case - that is, novel qualities could emerge?
With that said, I don't think that current LLMs are anywhere close to this category, but I just don't think this your reasoning is sound.