Isa 43:10 Ye [are] my witnesses, saith the LORD, and my servant whom I have chosen: that ye may know and believe me, and understand that I [am] he: before me there was no God formed, neither shall there be after me.
Though Peter may be used as a classic example of lack of faith as he denied Christ, faith is a different issue than knowing, believing and understanding.
Peter had been given a subtle revelation that Jesus was the Messiah, the son of the living God. Mt 16:16 He had a sure knowledge of that. He did not understand the need of the Messiah to die, and so it shook his faith.
He had done the works sufficient to know that he was the incarnate God, though they would not comprehend the true meaning of that until after the cross.
Their declaration that they know he is from God, precedes his declaration that they know. Joh 16:30
The declaration "You believe at last!" is the point at which he can be finished with the works of the disciples. He can sit (be finished) on the garments (works) of the disciples as he rides into Jerusalem on a donkey.
Now he can face the cross and trust they they will understand at some point that even the cross was the plan from God.