Consciousness is just a log file. It's our mind's representation of itself. Suppose we decide to eat something because we're hungry. What actually happens is a vast array of calculations in our meat computer considering many inputs and possibilities. However, once the "eat" action is selected, it summarizes all the calculations into "I was hungry so I decided to eat" and feeds it back into the meat computer as input for the next round of calculation.
Therefore, the only "proof" we have of no consciousness in the current LLM zoo is that they're all once-through.