Why does anything exist? Wouldn't it be more believable if nothing existed?

This is an interesting question. If you want to explore it through a text, I recommend Schopenhauer's On_The_Fourfold_Root_of-the_Principle_of_Sufficient_Reason or Wittgenstein's "Lecture on Ethics." Note that usually when we ask "Why?," we mean to ask how something is to be explained given some background conditions . But the question, "Why is there something rather than nothing?" precludes the background against which the "Why?" makes sense, and so might really not be a real question at all, so much as an expression of awe, or something. And if nothing existed, there would be nobody to believe it at all! Your existing is a precondition of being bothered by the question in the first place.