God does not exist.

In one sense, "God does not exist" is an accurate formulation of a very specific piece of Judeo-Christian doctrine, using a materialist's set of definitions.

Google "universe definition" and you will find that in several places — though it's not the only definition — the universe is defined as something along the lines of

"the totality of all the things that exist."

 There is no reason why you can't use such a definition of "universe" for the purposes of your argument.  It's just one way of drawing the boundaries around your system.  Draw it one way to solve Problem 1, draw it another way to solve Problem 2, just make sure you draw it usefully each time.

OK, what's that mean then to Christians?  If you find yourself in a discussion with someone where the ground rules of your discussion — you did  bother to lay out some ground rules, didn't you? – include the identification of "existence" as "part of the universe?"  

Isn't it obvious?  You cheerfully and clearly state that God does not exist.  Right?

Because you, being Christian and not pantheist or atheist, believe that God made the universe and is not, therefore, a part of it.  We have always maintained that.  If the universe is the set of all things that exist, then, God doesn't exist.

God must, then, do something else.

Transcends existence, maybe?  

Anyway, my point is that there's no reason a Christian can't have a discussion about the existence of God with a materialist on the materialist's terms.  Just be clear about it.  You will get nowhere, either of you, if one has in his head "existence = physical existence and membership in the physically observable universe" and the other has "existence = all physical things and also metaphysical truths and spiritual entities." 

This is so even if what you are arguing about is the existence of, say, right triangles.

Pick one and argue on those grounds.  "If existence is defined as 'membership in the universe,' then, no, God doesn't exist.  I believe God's not part of the universe; God made the universe and everything in it.  So a more fundamental question is, could there be — using the  term broadly, mind you — anything besides the universe?"  (Good luck trying to construct your discussion, I might add, without using the verb 'to be.'  I suggest you have recourse to some other languages.)

Redefining your terms can have interesting results, at least in your head.  If existence is membership in the physical universe, then God doesn't exist (He does something different — and why not?  Maybe that whole three-and-one-at-the-same-time thing works out better that way), and then, of course, neither do geometrical entities exist (have you ever seen a sphere?  I mean, a real sphere?), nor do emotions, or will, or ideas of any kind.  All those things, instead of "existing," do something different.  What is it they do?  Unwrap, and wrap your mind around it a new way, through a new use of your language.  Old familiar things look new:  the Incarnation, for instance.

Sooner or later, though, you're bound to come up against something that reminds you that you're really playing a game with words — a profitable game, I think, and a fun one, but a game nonetheless.  Wait a minute.  Remember the divine NAME?  "I am who AM?"  Didn't He kind of, you know, make a point of saying "Existence is mine?"  Huh.  Maybe it's better to say it's the universe that does "the other thing."   Still, next time I find myself discussing Life, The Universe, and Everything with a materialist, it might be edifying to step onto his semantic grounds.