Would a complete Theory of Everything prove there is no God?

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No. The gaps in which God can hide are way bigger than science, an empirical process that delivers empirically verifiable results, can know. First off, a Theory of Everything could not show how the universe was created. Second, it does not rule out the possibility of a ‘mathematical God’, or a god that can still exert effects on this world without really existing inside of it, the same way math exerts effects on the world without really having an embodiment.

There could also be gaps left by the Theory, one already exists in that it is impossible to deterministically predict the outcome of quantum interactions. With that alone, God could dominate mankind, shaping events to his whims, while remaining quite safe from detection. No theory of everything could reverse quantum indeterminacy.