This question can’t be answered unless we agree on a defiintion of “faith”. Is “faith” merely believing something exists? Or is “faith” defined by the action that occurs after recognition that something exists? James tells us that faith without works is not faith at all, so it seems to me that God writing “good night” in the sky may cause the world to recognize He exists, but it will not impede the free will of individuals to act/not act upon it and actuate that faith.
Here’s a great case in point: Proof of God’s existence did nothing to limit Satan’s ability to choose “self” instead of “Other” (God). So proof would not in any way impede free will. One cannot, as Protestants contend, simply believe something and be saved. Since the fruit of faith is works undertaken by free will of man, God showing up on a streetcorner and screaming “I’M HERE!” does not preclude faith itself, since faith requires a response from its subject.
And, as in the case of Satan, it’s conceivable that proof of God’s existence may yield less faith, not more, since man, in his fallen nature, has a proclivity to choose “self” over “Other”, regardless of the circumstances.