Let's be honest

[Belacqua]

Theologians would say that it's valid but not sound. 

That is, given the premisses as written, the logic works -- therefore it's valid. However theologians don't agree that God is "an existent entity." So for them it's not a sound argument.

Fair enough, however. One definition of God is Necessary Being. Therefor the answer to the question of why there is something rather than nothing starts to sound tautalogical, a point @emjay makes. To me this is not an insurmountable objection. Because the something in question is not simply nothing but also (apparently) not everything that could be. In other words, we have to ground the particularity of this reality on transcendent universals...eternity in a wildflower.

Yeah, I think I was too limited in what I said before. I was thinking of "existent entity" as an existing object, which exists in the same way as other objects that we know. So for example if I started a list of all the objects in the universe, it might go: "my left shoe, the Statue of Liberty, Jupiter, God, my right shoe, etc. [to include everything in the universe]." But as I understand it God doesn't fit on that list, because God isn't a thing you can count up alongside other things. He is essentially prior to all of them. 

But yes, if we think of God as a transcendent universal, and it's OK to say that such things exist, then you'd say that God exists. Just now I looked up "necessary being" on the Stanford site, and they use "entity" to refer to non-concrete things, so I was wrong to limit the word that way. They say:

There are various entities which, if they exist, would be candidates for necessary beings: God, propositions, relations, properties, states of affairs, possible worlds, and numbers, among others. Note that the first entity in this list is a concrete entity, while the rest are abstract entities.

I think I disagree that the God of classical theology is a "concrete" entity, but maybe I'm misusing the word again.

I don't think it's proper to say that "God created existence" though, as if that's a thing that happened at a given point in time. I don't think we can talk about what existed before there was existence. So @HappySkeptic, I'm going to apologize and change my answer: theologians would find your syllogism unsound because they reject the premises. They hold that God is existence, and a necessary being for the existence of anything else, so they don't believe that there was a time before the existence of God. (Augustine addresses this at length.) 

Quotes from Blake always hold a lot of sway with me. As I understand it, he thought of God as infinite. And (before Georg Cantor came along) people thought that infinity could not be divided. You can't cut infinity in half -- if you drew a line through the middle of infinity, it would extend out in one direction to infinity still, so it would still be infinity. Therefore if God is present in a wildflower, it's not as if a part of him is circumscribed in that flower; he is present in his entirety in that wildflower. It's the fault of our doors of perception that we can't see that. So for him and others who hold to this line of thought (e.g. Nicholas of Cusa) it's wrong to say that there is something where God is not. 

So Blake wrote this to the false God of this world that other Christians believe in (who can be divided or absent):

To God 

If you have formd a Circle to go into 
Go into it yourself & see how you would do