Again Monsieur, you said God gives faith to the believer. If God gives it to the ones who believe, then someone has believed without having faith. You have the effect before the cause.
Look, I agree we have faith in our spouse, a car, a plane, a family member, &c. That is a carnal/fleshly/natural faith. Yet, that faith saves nary a soul. The supernatural faith God gives via the regenerative power of His Spirit is what effects salvation.
You are simply drawing a conclusion based on pre-conceived facts. You have no scriptural basis for your position. It is the Calvinistic position but it is not scriptural. No one here has yet to back it up with scripture. As I have demonstrated Phil.1:29 fails to do that. It is directed to Christians, not to the unregenerate.
Faith that saves a soul always has Christ as its object, not a car, a plane or a family member. That is why it can save. Furthermore, faith is intangible. The work is the work of the cross. It must simply be received by faith. Just as a child receives a gift from his or her parent, so the unsaved receives salvation, the work of Christ by faith as the gift of God. It is salvation/eternal life that is the gift, not faith.
If faith is faith, then the unregenerate who end up dying in their sins possessed a fruit of the Spirit, yet died lost. That is why faith is not faith, in that they are all not the same faith.
Faith is faith by definition: trust, confidence, belief. You have confidence and trust in your wife don't you?
Even the unsaved can say that.
To use a parallel illustration: One cannot deny that love exists before salvation. A man will love his wife. He will love his parents and other relatives. He will love material things as the rich young ruler did. The object of his love may be something other than Christ.
However, when he becomes saved, the love for one's wife does not diminish, but ought to grow greater. You still love your wife don't you? (I am only assuming you are married). So what is the difference? The love that you have now has a spiritual aspect to it. With a love for Christ (even though your love for Him ought to be first and foremost), He enables you to have an even greater love for your wife.
The same is true with faith. Man has faith. When he is saved that faith then has a divine or spiritual side to it. He becomes more discerning. He is able to put his trust more in Christ and less in other things of this world. That doesn't mean that his "faith" in the ability of his car to take him to the other end of the city has diminished any, or that his confidence in the airline has diminished. It may make him more discerning in choosing an airline. God gives wisdom along with faith. If in a journey he runs into trouble, he now, by faith, has the Lord to rely on. God gives him peace instead of anxiety. These "divine graces" as you call them are accepted by faith. They are not available to the unsaved. Thus faith is divinely enabled for the saved.
Salvation is by faith, not the faith of God but accepted by man's faith. Jesus said "according to YOUR faith so be it."
"Believe" on the Lord Jesus Christ and thou shalt be saved." The "belief" was the jailer's faith, not God's faith.