First of all, it would have to be isomorphic to the universe minus the Turing machine, or you have an infinite referencing problem.
I have studied this for decades and find the whole thing riddled with false assumptions.
The mind/brain is part of the universe and it participates already in all that reaches consciousness, it does not sit God-like outside the rest of reality.
This situation ignores all development of the world to something higher. The Philosopher Bernard Lonergan has written on this in "INSIGHT" . I think most Turing fans subscribe to what Lonergan calls the mistake of thinking knowledge is 'the already, out, there, now, real'
Where is the place of WILL in all this, of FREEDOM.