I can only say what he is not. I doubt his omnipresence most of all. The fact that he is considered to be 100% pure means that he cannot be evil, so in this sense he can not be everything. If this were then the next aspect that falls in line is that he isn't everywhere, because he cannot exist with evil, or rather evil cannot exist in his presence. This means that either everthing on this earth is not evil, or he is not omnipresent. Society however would say that this thought is atrocious as how could murder, or the like ever be thought as good, or at the least neutral. I doubt our ability to understand what everthing means, when we say that "he can do everything" our thought of everything is all-encompassing, but we don't realize what we say when we describe Him as such. It would seem that we put all our eggs in one basket when we describe Him.
All of this being said I still believe he can speak to us through 'timing' the fact that events happen at specific, uncontrolled times is a great example of a higher power. I believe that he could not have manifested within himself, this brings in the idea that something bigger than God exists, of course this is only greater than our perception of God so if something greater than God exists perhaps that what God really is... who knows?