Maybe it's possible to run AGI on a Turing machine, maybe it's not, Arguing from ignorance, of course nothing is knowable for certain. However there has been a

Maybe it's possible to run AGI on a Turing machine, maybe it's not, Arguing from ignorance, of course nothing is knowable for certain. However there has been a lot of work on the universality of Turing machines, showing that a Turing machine can simulate any conceivable concept of finite computation and can approximate any conventional physical system. I think a more useful way to express your intuition is to note that if human-built AGI comes into existence, it might be runnable on a Turing machine but quite possibly not efficiently so.