I would like to know your theological or denominational context because it is amazing that two people can read the same scripture and come to such completely different fundamental interpretations. I am a Latin Rite Catholic. For me Faith is the response to God's universal call to Salvation and is therefore an act of the will. It does not spring from premise, reason, or intuition, nor is it imposed by God. Faith is the belief in things not seen, not known and often not knowable.
Peace be with you.
Faith is belief...full stop.
There are things one believes or has faith in that one did not necessarily "choose" to believe i.e. you exist, you have a natural father, you have 10 fingers, the sun is shining. Belief is not always an act of human "will". There are many examples of our believing things without the "exercise" of faith.
Did Paul "choose" to believe that God had struck him down and revealed himself as Jesus or did that happen outside of an act of his own will?