God does not believe for them. They, being dead in transgressions and sins can not believe. Once divine quickening takes place, they believe, now having Spiritual life, and an ability to exercise faith and repentance.
Wrong definition. They are not dead, as in a corpse, totally unable to respond. If they were then Adam would have not been able to respond to God. God said to Adam: "In the day thou eatest thereof thou shalt surely die."
Adam ate; Adam died.
Then Adam, being dead, proceeded to carry on an audible conversation with God. Your theology says this is impossible for Adam is a spiritual corpse. But he is not. He is simply spiritually separated from God, and therefore able to respond to God. He is not restored to fellowship with God until the blood of an animal is shed, "for without the shedding of blood there is no remission of sin."
Tell me:
How can a dead Adam being dead still continue to talk to God?
The answer: Death simply means separation from God.
Any man is free to call upon the name of the Lord. He always was until Calvin told you differently, but that didn't change God's mind.
And then we have this interesting Scripture:
Genesis 4:26 And to Seth, to him also there was born a son; and he called his name Enos:
then began men to call upon the name of the LORD.
--What was the impetus here?
Even MacArthur makes an interesting comment here:
men began to call on the name of the Lord. As men realized their inherent sinfulness with no human means to appease God's righteous indignation and wrath over their multiplied iniquities, they turned to God for mercy and grace in hopes of a restored personal relationship.
They turned to God, he says. How do men turn to God? In faith of course.
"But these are written that you may believe that Jesus is the Messiah, the Son of God, and that by believing you may have life in his name."
The very scripture you use, denies your position, but you are too blind to see that.
John 20:30 And many other signs truly did Jesus in the presence of his disciples, which are not written in this book:
31 But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.
John records that Jesus did many miracles. The other gospels record about 35, but the Gospel of John centers around seven specific miracles. Why? These miracles are are recorded "that you might believe that Jesus is the Messiah." They demonstrate the deity of Christ and have a purpose to bring one to faith in Christ. Note it is their faith in Christ. Nothing is said about any divine faith. That would have to be read into the scripture just like the RCC reads into the scripture baptismal regeneration and infant baptism. The faith belongs to the individual, the unsaved individual. Nowhere is it even implied that it is given by God.
That YOU might believe that Jesus is the Christ.
Now, having done that, you might continue to believe to believe. The Christian life is a life of believing, a walk of faith. But it starts out with one believing or having faith in Christ. Don't read more into scripture than is already there.