If God gives us faith, by grace, we cannot say no to it. We don't have the power to reject what God has already done.
If a person buys you a brand new Corvette, but you refuse to drive it, does it make the car any less yours?
No. It just means you refuse to use the gift you have been given. We all are guilty of not trusting what God has given us. But, that doesn't remove the gift.
When God wills to do something for us, he does what he wills to do. Best example is Paul's conversion on the road to Damascus.