In my opinion, determinism is a feature that appears in all conditioned phenomena (at the very least, in all phenomena of our subjective experience), which makes those phenomena follow inconditionally causality and conditionality.
With X set of conditions, Y consequences occur; Y depends on X to arise.
Some fact or state of affairs A leads to a new state of affairs B; B is caused by A.
This order of things is what allow us to predict events, to manipulate circumstances, to increase our chances of success, and to achieve desired outcomes. Both Dhamma and science follow this, with the former having the main purpose of attaining liberation from dukkha and the cycle of rebirth.
What the Dhamma training does, in my view, is not to "bypass" determinism, but to change what factors are decisive to give rise to interpretation, subjective experience, intentions and deeds. Instead of being governed by the "imposed" interpretations of others, becoming ourselves trained and habituated on such interpretations; becoming ourselves replicators of such interpretations; producing intentions and new interpretations from such habitual and learned interpretations.
Right View is key for all lf this: RV is achieved by reasoning or by influence of others, which leads to acquiring or producing new information that could make our interpretation not giving rise to afective and cognitive contradictions between expectations and facts.
With Right View sufficiently developed, other mental factors and qualities start developing as well, while others become diminished in its presence and influence. This makes one's own critical judgement, reflection and knowledge (both led by the wisdom we have cultivated previously) to have be more preponderance when taking decisions or intending something, or to put ir from the opposite perspective, allows us to not get blindly and impulsively influenced by old habitual patterns, by others' opinions, by unsupported assumptions, by the worldly winds, etc.
I wouldn't summarize all of the above by stating that the mind becomes predominant over the external conditions. This is because, without exceptions, it is the mind the one that give rise to mind states. As long as there is the conditions for the arising of intentions, intentions will arise, choices will be made, and deeds (thoughts, communication or bodily acts) will be executed. The question, then, is what factors and conditions are responsible for the arising of intentions as it arises in some specific context.
Instead, I'd summarize all of the above by saying that the training in the Dhamma strenghten, develops and takes to fulfillment the factors that give rise to wisdom and mindful living, while weakening, diminishing and eradicating the ones that lead to ignorance, acritical and impulsive lives.