Can God love?

[Angrboda]

Unless being so is impossible.  It's routinely acknowledged that God can't create square circles.  What relationship you see between God being the "I am" and this question is something you'll have to elucidate more completely.  If all you're saying is that God can do anything he wants to do, then most would disagree with you on that point.  So you need something more specific than what you've claimed here.  You'd have to start by at least clarifying what it means to be both God and man.   If being God and man is fundamentally incoherent, no amount of Alpha and Omega will get you there.

More importantly, it must square with Christian theology, and the bible, else you're just wasting your time and mine.

well one, I don't know anyone who would disagree that God could do anything He wants to do. again.. that is the definition of alpha and omega.

The omnipotence paradox is a family of paradoxes that arise with some understandings of the term 'omnipotent'. The paradox arises, for example, if one assumes that an omnipotent being has no limits and is capable of realizing any outcome, even logically contradictory ideas such as creating square circles. A no-limits understanding of omnipotence such as this has been rejected by theologians from Thomas Aquinas to contemporary philosophers of religion, such as Alvin Plantinga.

Wikipedia || Omnipotence paradox