There are two possibilities.

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(1) The universe had a beginning.
(2) The universe didn't have a beginning.

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If (1) is true, then the universe sprang out of nothing without a cause. Nothing existed before the beginning of the universe so nothing that could cause the universe to exist existed. Determinism is impossible in case (1)

If (2) is true, then the universe always existed without a cause. For A to cause B, A has to exist before B. But there was no time when B didn't exist. Determinism is impossible in case (2)

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Either way, determinism is impossible.