I asked myself a couple of additional questions, anwers are welcome:
1. The issue of counterfactuals
If we take it at face value that ultimate reality operates strictly deterministic, then the whole machinery leaves no room for errors. Literally everything plays out just as the laws of physics demand it - without any exceptions. If we imagine that world to be free of any living and thinking entities, everything happens just the way it should, without errors.
But if we now include human thinking and deduction into that reality, the picture suddenly changes, since people make errors, they can take counterfactuals as facts and vice versa. This means that the human mind - deterministically produced by the laws of physics - often produces ontologies that are nowhere to be found in a strictly deterministic world: the human mind can produce all sorts of things for those we can say that they do not exist.
Consequently, if that strictly deterministic world view is true, parts of the deterministic machinery (the brains) are able to produce false statements about the whole machinery (or about parts of it). This seems to be no wonder, since these parts are not the whole and therefore these parts lack some information to produce the correct statements that reflect the whole reality correctly instead of filling the gaps with some imagination. Nonetheless we have to state that a strictly deterministic world obviously is able to produce counterfactual, non-existent things by acts of imagination and thoughts. What is non-existent are not the thoughts themselves, but their thought-to-be-ontological contents.
So, physical laws in a strictly deterministic world obviously can and do produce thoughts that often are in contradiction with these laws themselves. This can be easily seen when evaluating the huge amount of scientific papers on the "market" whose conclusions contradict each other. From a logical point of view, they cannot all state the truth about (ultimate) reality.
So, the strictly deterministic world that has been defined by us as working error-free is nonetheless able to produce errors. It does not produce these errors on the fundamental level (particles, trajectories, interactions etc.), but on a more complex level (brains). The term "errors" surely is a human term, relative to the human desire to know and value truth more than falsity. Nonetheless we can ask whether it is possible to minimize these errors down to zero in the future?
If the reason for these errors is that parts of ultimate reality (brains) cannot represent the whole thing (due to lack of the whole information, the whole truth), then only the whole thing may be error-free - as is expected within the framework of strict determinism. Now, the whole thing is considered to be inanimate and does not know everything about itself (but only what human brains know about it). The more astonishing it would be if parts of that whole thing (brains) nonetheless at some point in time should be able to know everything about that whole thing (theory of everything). Notice that without animate matter (consciousness), the whole ultimate reality wouldn't know anything, not even that it exists! But with brains, so the story goes, ultimate reality will sooner or later know everything about itself (at least everything foundational, what would be a lot!).
Therefore let's look closer at what inanimate matter doesn't know - but human brains know (in the sense that these brains know what they [still] do not know): if there was a big bang, are the initial conditions that led to the present world have been a necessary consequence of some other deterministic processes - or have they merely been a realized possibility amongst other possibilities? How can one ever solve the problem of a "beginning" other than to assume that there was no beginning, but ultimate reality literally did exist forever (maybe in a timeless realm, maybe only in a realm where time was, is and will be "present" forever)?
If we can't trace infinitely back into the past, how substantiated is the assumption of a strict determinism? Moreover, if we assume ultimate reality with a certain set of physical laws to be eternal (without a Big Bang), how would that leap of imagination be different from assuming a Creator for our present world? The fact that the laws of physics were what they were (and not other) and are what they are then is equally mysterious than believing in a Creator.
2. Quantum fluctuations
Are Quantum fluctuations real? And if yes, do they act deterministically or do they counteract the course of events dictated by the known laws of physics?
3. Non-measurable parts of ultimate reality
Are there in-principle non-measurable, non-deterministic influences in ultimate reality that we never can detect in a repeatable fashion? Are there even aspects of ultimate reality that never can fully be imagined by human brains?
4. What place has "intelligence" within the world view of a strict determinism? How can - and should - "intelligence" be defined within this world view?