The gift & working of grace

why would an unbelieving person begin to believe? What brings about this change?
It is the unseen power of God, working by his Spirit, in the soul of the individual.
This is what is described under the heading of 'effectual calling'

Catechism 31
What is effectual calling?
Effectual calling is the work of God's Spirit, whereby, convincing us of our sin and misery, enlightening our minds in the knowledge of Christ, and renewing our wills, he doth persuade and enable us to embrace Jesus Christ, freely offered to us in the gospel.