The fundamental problem with the argument is that, contrary to the second and third premises, an omnipotent God who is the ultimate Creator CAN know His his relationship with reality, for the very reason that all manifestations of reality are ultimately derived from Him. Absolutely no evidence is adduced when Berg asserts that "there is no way of obtaining such certainty." I'm pretty sure that I cannot ascertain my holistic relationship with reality, but it is a far cry to assert that God, who Berg defines as omnipotent, omniscience, and the ultimate reality, among other things, cannot do so.
Argument 5: The Universal Uncertainty Argument1. An uncertain God is a contradiction in terms.
2. Everything in the Universe must be fundamentally uncertain about its own relationship to the Universe as a whole because there is no way of attaining such certainty.
3. Therefore even an entity with all God’s other qualities cannot have the final quality of certain knowledge concerning its own relationship to the Universe as a whole.
4. Therefore God cannot exist because even any potential God cannot know for sure that it is God.
Note: Stated as a logical paradox this argument is ‘God cannot exist because God cannot know for sure that it is God’.
To make matters worse for Berg, his argument would prove nothing even if it were true. Perhaps God couldn't ascertain His comprehensive relationship with reality - again, a stupid point, but lets assume it for the sake of the argument - but he could no doubt acquire part or even most of it. It wouldn't take ten seconds for an omnipotent God to realize that He is extremely powerful and can rule over anything. If mere mortals in the past (and present) have believed they are god because of their power, then it is not hard to imagine that an infinitely more powerful being than Alexander the Great would arrive at a similar conclusion, with the added benefit that it would be a correct conclusion.
Berg trying to argue that knowing with 100% certainty is an essential but impossible attribute of God is tantamount to arguing that 100% certainty is a logical contradiction. But most theists would admit that God cannot perform logical contradictions. His argument is no more sound and applicable than the argument that God cannot be God because He can't create a circular triangle or a married bachelor.
It's bad enough that Berg's argument is incorrect, but to advance something that proves absolutely nothing makes Berg able to live up to the lofty standard of nonsense he set with his other arguments. It'll be difficult for him to outdo his poor performance with the next one.