Also, faith is not a work (Rom.4)
God saw that they would have faith and their works would follow that faith.(James 2:21-22)
Faith is a gift from God.
Eph 2:8 "For by grace you have been saved through faith; and that not of yourselves, it is the gift of God;"
If God looked down the "time tunnel" to see their faith, the only thing He would see is the gift He had given them.
And you're still left with the clear fact that man's "foreseen" faith is what causes God to choose him, so the cause of the choice is not in God, but in the man. You make God's choice a reaction, and not an action initiated by God from within Himself, Who is the First Cause of all that is.