Is it always possible to find a mapping under which the iron bar seems to run the program consciousness.exe? That is not obvious. Let's say the Turing machine

Is it always possible to find a mapping under which the iron bar seems to run the program consciousness.exe? That is not obvious. Let's say the Turing machine has states T, and the iron bar has states B. The program consciousness.exe is a dynamical system on T, called t: T->T, and the iron bar is a dynamical system on B, called b: B->B. Both of those functions/dynamical systems are given, because we observe them. What the triviality argument says is that for a large class of "obviously non-concious b" there exists a (bijective) mapping F: T -> B such that t = F^-1 o b o F no matter what t is. Is this true? Consider the cardinality of the set of functions/programs on T. It is |T|^|T|. What is the cardinality of the set of bijective mappings between T and B? It is min(|T|!, |B|!). Much smaller! Therefore it is not at all obvious that Alice, Bob or Claire or any of their friends will find such a mapping, even if the methodically try all of them. This seems to me an issue with the presented argument. Although personally I still think consciousness is a physical phenomenon we just have not mapped out yet. Like magnetism or radioactivity before they were properly explained.