So God initiated before faith existed?
Here is your twist, which is false. The ungodly do not have faith therefore it cannot be righteous.
By grace alone, yes.
Once grace is provided, faith is given.
You cannot say "alone" to two different things. That would be a dual thing, not an alone thing. Here you twist your theology.
If God never initiated the relationship with Abram, would Abram have believed?
Agreed, Abram's faith had nothing to do with God's covenental grace bestowed upon Abram.
Correct, human faith has nothing to do with God's gracious choice to save. Faith is an effect of God's gracious salvation of the sinner. "Even while we were yet sinners..."
Since we are chosen on the basis of faith, how do you suppose God chose an individual to give them faith.
Through faith requires faith before being chosen and saved.
Our faith provides our access to the grace in which we stand.