Every single event we cannot accurately predict represents one of two conditions (or a mixture of the two):
1. a lack of information or ability to process that information on our part
2. true randomness
The only way to empirically prove that an outcome is predictable is to accurately and repeatedly predict it. Therefore, the only empirical proof of absolute
determinism would be to demonstrate a flawless method of universal prediction - a precise theory of everything - that approaches perfect reliability across an extremely wide range of ongoing systems of causation.
Strong induction and the progressive track record of math and science would appear, according to Occam's Razor, to make determinism a highly likely scenario. However, for this to remain true on an absolute level (not even as proof but as strong likelihood) we must first assume what may very well turn out to be a false dichotomy. Many strict determinists present an either/or picture of the universe that says either determinism is always true or it is not true at all. Since we can see it in action in so many ways, it must, therefore, always be true. While this represents strong induction, it is not empiricism.
For one thing - we can never empirically witness an effect without a cause because we will never be able to recreate the conditions that caused it - since it was not caused. Therefore, any effect with an unknown cause, could represent an effect without a cause. The minute we can precisely reproduce an effect - then we know it can be caused. Until then, we can only assume it must have a cause. Therefore, a causeless effect is not falsifiable. The burden of proof is on the affirmative claim - which, in this case, would be the claim that a particular event had a cause. The singularity that 'preceded' the Big Bang is a prime example of an event or condition that must be proved to have a cause, or we must assume that it did not have a cause, since the burden of proof is on the claim that it did have a cause.
String theory suggests that eleven dimensions may be necessary to contain the 'causal gestalt' that would describe a version of an absolutely predictable universe. Dark matter and energy might help explain why the universe appears to be expanding the way that it is - yet we can't put our finger on that yet either. We still don't know why matter has mass. Why is gravity an asymmetrical force? Why does time appear to be a one way dimension? How did so much matter survive and so little antimatter? What about the horizon problem? There remains a great deal of mystery in the universe. Some of it may be unsolvable.
So, at this stage of the game, absolute determinism is not empirically proved or provable. And, if there is the possibility of completely unpredictable events - then there is the likelihood that those unpredictable events entered the causal gestalt - because they are likely to have deterministic effects which, in turn, become causes.
Since the causal gestalt is intertwined throughout everything (the iron in my hemoglobin that carries the oxygen to my brain so I can think originated in the furnace of a supernovae many light years away, for example), any degree of randomness in the causal gestalt represents some degree of randomness in the collective components of that gestalt that is me. This includes any random aspect of environmental stimuli that my consciousness encounters and is shaped by as a result of that encounter.
Thus, we can talk about relative determinism, or virtual determinism, or practical determinism, or even deterministic probability and be reasonably certain we can rely on it. Perhaps we are compelled to. But, as long as there is any possibility that some things happen for unpredictable reasons, human beings are likely to behave, to some degree, unpredictably as well.
If this unpredictability is actual, then it may very well be that our emerging consciousness becomes, through evolution, better and better at adapting to some degree of utter unpredictability even as we become better and and better at predicting outcomes. This adaptation could be seen as true creativity - an actual ability to extemporaneously adapt to completely unforeseeable events.
So, we are left with little reason to abandon the possibility that our words and actions might be just a little bit more than the inevitable toppling of dominoes into each other. So far, the argument against adopting an existential perception of actual agency is not airtight.