WIY –
My point is that obviously Hashem feels that there is sufficient bechira even in a world that knowledge of his existence is certain. In fact, that is the ideal world, as is evident in our yearning for mashiach. (And as you said, people make bad decisions even when they know what’s right.) Therefore, having the world appear to be billions of years old is completely unnecessary. Ergo, saying that the reason the world looks that old is for our bechira, is at best a cop out.