If what you say here is true then ABSOLUTELY EVERYONE would be saved. Is that not what God wants? So hear the words of Christ (John 3:17): For God sent not his Son into the world to condemn the world; but that the world through him might be saved. The "world" here is the world of humanity, and the lexicons and John Calvin all agree that this is so. Therefore according to your theory, not one person should be lost.So we literally have faith, put there by God, that is dormant, and then drawn out by the hearing of the Gospel.
But what does Christ say next which is confirmed by John the Baptist? John 3:18, 36: He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God...
He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him. (This corresponds to Mark 16:15,16).
So you can see that it is the Gospel and the Holy Spirit that GENERATE saving faith, and not all will believe in spite of that, because the resist the Gospel, and love darkness rather than light.