Yes! This! Wonderful, you put your thumb right on it--you had a crisis of word choice, not of actual faith. Proof means you do not need faith!
I'm not sure why God would *require* faith, we just have the reported word of the prophets and various believers and a long line of theologians in various religions of The Book all claiming this. Many of them like to argue why God needs faith, too.
I applaud the clarity of your thought process here.