Thank you for your question. This is not an issue that is to be proven in a logical sense as it is a presupposition. Presuppositions are judged according to their coherency, consistency, explanatory power and their implications (for more on these criteria please refer to the field on analytic philosophy). As such to discuss free will one would have to look into both the implications of free will and of determination and consider that within the framework they are using to understand a number of other questions. For this reason, the traditions that we have explaining the necessity of free will focus on the injustice of reward and punishment without meaningful free will. This is an appeal to the lack of consistency of determination with the Justice of God in meaningful judgment and also to the implication of pointlessness in His testing His creation.
May you always be successful