I don’t expect that I’ll be able to be all that earnest—frankly, I don’t have much expectation of anything supernatural happening or even much desire for God to exist—but I’ll have a go. To any Christian who says that I’m not approaching this with much sincerity, you’re right. As I read it, none is required—as it should be. Sincerity comes after the fact; sincerity is earned.
Well yes, sincerity does matter. If you are not interested in God's Revelation or what he wants from you, then there's no point in him revealing himself. He won't waste his time.
However, if your heart is prepared to be changed, then it increases the likelihood of him revealing himself to you.