One has, I think, to go through a conceptual turn-around in general ontology somewhat like the one Newton executed for physics. Aristotelian physics made motion problematic and rest unproblematic. The question then was: "Why is there motion (here, or there, or at all) rather than rest? Newton saw that motion was no more problematic than rest. What had to be explained was change: from motion to rest, or conversely. Similarly, in general ontology one has to understand that existence is, in general, no more problematic than non-existence. Existence isn't somehow "harder" or inherently less likely than non-existence.
-Dallas Willard, "Language, Being, God, and the Three Stages of Theistic Evidence", in Moreland, J.P. and Kai Neilsen, Does God Exist? The Great Debate (Prometheus, 1993).