There is nothing in classical physics that suggests the universe is deterministic on cosmic scales. There's plenty in physics which suggests it isn't.

If you want to propose any form of determinism, be it superdeterminism, a bulk universe, or any of the other popular variations, you have to start by proving that causality is infinitely precise and absolute. Because otherwise your causality is partly random and therefore not truly causal at all.

Our experience of causality suggests that real measurements have limited precision, and predictions can only be made on limited timescales.

So anyone who is proposing superdeterminism is claiming that this can be fixed - by hidden variables, with noise-free super-realistic precision, which allow a universe-wide predictive horizon.

Free will is a side issue here, because the problem doesn't go away even if the universe has no observers.

The problem isn't whether free will hides super-predictive hidden variables, it's whether it's plausible that super-predictive hidden variables exist at all.

If you believe they do, you have a first-order universe in which these mysterious entities operate with effectively infinite precision behind the scenes, to create a second-order universe which has limited precision in practice.

Of course that may be happening. But it seems like quite unlikely.