This response assumes you to be asking whether or not a human is able to experientially distinguish between a deterministic universe devoid of free will and a non-deterministic one in which free will exists.
Given only one of these options is likely to be true (ignoring other options for a moment), and given the fact we don't know for sure which is true, it seems any means by which we could arrive at anywhere close to discernment will incorporate some degree of imagination.
If a person can suspend judgement for a moment as to which 'reality' is true - a difficult task - one can begin to experience life more and more as the 'ride', the inevitable unravelling of events, that would ensue from purely deterministic processes.
This is where meditation can prove of use. Meditation equips a person - via the diminishment of external stimuli - to pay more attention to the way thoughts arise 'out of nowhere'. The meditative experience can then be carried over into the 'day-to-day' experience via mindfulness techniques, which enable a person to retain this sense of being 'separate from the thought', 'separate from the emotion'. This in turn provides insight as to how, when we are not aware of this separation, our behaviour is largely (if not always) causally determined by mental phenomena such as thoughts, emotions, desires and so on (This likely goes some way to explaining Buddhism's adherence to a deterministic world view).
Once this is achieved, it is far easier to begin to achieve the discernment about which you enquire; between the aforementioned 'ride' (the deterministic experience) and the typical self-directed/controlled experience.
The ramifications of this discernment can permeate a person's daily life quite profoundly. The mindfulness (essentially an increased awareness of one's mental processes), equips us to exert greater control over the way we react to stimuli, and to view our own behaviour (and therefore the behaviour of others) without condemnation. It becomes easier too, to view each other as unique embodiments of predetermined circumstance equally deserving of compassion and respect, to shed notions of virtue and immorality, and to be far more grateful for our relative good fortune.
For the meditation-averse, this thought experiment can provide a quick, accessible and powerful experience of deterministic mental processes: https://www.youtube.com/watch?v=UwjD4hfrDsg).