To my knowledge it is quite widely accepted in the scientific community that at the quantum level physics is not deterministic, only probabilistic. I know that there were some efforts to find some hidden variables at play that could make quantum physics deterministic. However after Bell's experiment was performed, the chance that hidden variable is at play was diminished. Therefore we often hear that quantum world is truly random.
However even if hidden variables are not at play, I wonder whether we should accept this view that quantum effects are truly random. Why? I will give you an analogy: Let's say we have a pseudo-random function that generates numbers. The numbers it generates seem to be random even though they are not. If we only see the numbers it generates, it is impossible to find some hidden variables at play. Could the same be true about quantum randomness? Maybe at the beginning of the universe there was some "function"/mechanism by which the universe would behave. However this mechanism is pseudo-random and therefore we are not able to find any hidden variables at play even though the mechanism is at the roots deterministic.
I wonder whether my reasoning is correct and therefore even if there are no hidden variables at play, we shouldn't rule out the chance that quantum world is at the roots deterministic given that there is a chance that some pseudo-random mechanism is at play and this mechanism cannot be determined from a pure observation of the nature? Or does Bell's experiment rules out even this kind of determinism which is inherently hidden from us?