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If the universe were deterministic (determinism, understood as the ability to accurately foresee all properties of universe at arbitrary time (or "time-space")), would it mean that God cannot exist (since it would not be able to change the state of the universe at a given time)?
Source: mentioned in the "Short history of time" from Stephen Hawking
If the universe were deterministic (determinism, understood as the ability to accurately foresee all properties of universe at arbitrary time (or "time-space")), would it mean that God cannot exist (since it would not be able to change the state of the universe at a given time)?
No. The Simulation Argument appears to trivially demonstrate that a deterministic universe presents zero problem for deity, or for less-than-deity. For our reality could easily be a simulation (e.g. we could be in The Matrix), run by beings outside the simulation. Such a simulation could be a block universe. Given such a universe, a 'change' to it would appear to force a re-simulation from scratch, which would mean that the previous, unchanged version simply ceases to exist.
Whether the argument as you present it works seems to depend on two assumptions.
First, this depends on a certain claim about what it would mean for God to interact with the universe. Specifically, it seems to require that God not be able both simultaneously know what will happen and be involved in what will happen. This assumption does not make much sense to me.
Maybe there are some missing premises that will shore it up? Best I can guess would be one of two routes. Either we need premises about God creating to the effect that God would need to create perfectly. In other words, God's intervention would demonstrate incompetence in creation. (I think this route of argument against God's existence is one of the more common ones -- but it only could prove that God is not good on a regular definition if it works).
Alternately, this seems to depend on some sort of claim that God's action would lead to contradiction or problems related to God's knowledge. In other words, if God acts to stop X, it changes the content of his knowledge of the future problematically. But I would need to hear it fleshed out some more to know if this is the route of the objection. The main response would be to look at counterfactual knowledge. In which case, God knows everything about every possible set of events that occur, so God intervening doesn't undermine his knowledge but merely specifies the path of possible events. This can be joined or not joined to God having a timeless view of history whereby God experiences them as all past.
The second assumption seems to be that God must be interactive. One could posit a God -- perhaps like Aristotle's [thought thinking itself] -- that doesn't interact with the world. In which case, there's no contradiction, because God doesn't care what people do to themselves or what happens to them. (This is one of the more Platonic moments in Aristotle's thought because the perfection of Aristotle's God depends precisely on God thinking only the essence of absolute actuality and thus being fully actualized).
But maybe I'm missing something since I'm depending on your summary?
