I appreciate the good faith engagement (cue side glare sigstoat), and I'm in agreement with everything but the use of "never" in the your closing sentence.
> There was never room for any non-deterministic thing to magic itself into the system
Depending what you mean by "into the system," existence itself is a glaring counterexample.
How did any of it get here in the first place?
Was there an uncaused cause?
Is entropy reversible?
Until we can explain-away these types of questions, it'd be prudent to remain noncommittal on the topic. The type of determinism that sigstoats expect might not even make sense in other regions or eras of reality. Things get profoundly hazy past Planck Era.