What Is Existence?
In the hopes that we can get off of* this detour, let me say what it means, and what it doesn't mean, to exist or to be real, for the purposes of the OP.
Briefly put, reality does not depend on my opinion of it, or my thinking about it -- caveat: my thoughts are real, and it's possible to detect brain activity associated with thought, but the fact of their existence does not depend on my opinion about them. Reality, while it includes my thoughts and dreams and such, does not change at my whim.
The distinction between the idea of a thing and the thing itself is crucial to our discussion. There is no doubt that ideas of God, concepts of God, exist. But since theists do not contend that God is merely an idea in their heads, but something which is and which acts in the wider world, then we do not need to concern ourselves with the reality -- the "thinginess" -- of thought itself; that is irrelevant here.
There are many things we have not detected, and it seems there are things we cannot detect in principle, such as things outside the "light cone" which defines the limits of our perception of the universe.
So what about these things? What statements can be made? Do we have to fall into the trap of either denying their reality because we can't detect them, or positing that any-and-everything could exist in this space?
No, we don't. We can use a simple process to determine what must be there, what could possibly (though not necessarily) be there, and what cannot be there. We take what we know, and we deduce.
If verified models of the world (in other words, theories that have been thoroughly tested, such as atomic-based chemistry) require that a thing exist in spaces we haven't explored, then we posit that this thing is real, even if we haven't found a way to view it yet.
If a thing is proposed, and it does not violate what we know about the world, and there is no fatal objection to the proposal -- e.g., it is not self-contradictory, or fatally vague, or mere gibberish, etc. -- then we are left saying "maybe". Not too satisfying, perhaps, but meaningful, and what else can we do?
If the thing proposed does violate what we know to be true (not what we merely assume, or deduce from incomplete information), then it's unreasonable to assert its potential existence merely on the grounds that we don't know everything or haven't looked everywhere.
Also, if the proposed definition of the thing is indeed self-contradictory, or so vague that no meaningful statements can be made about it, or mere nonsense, then no sensible claims may be made about it at all. Therefore, a claim to existence or reality is unwarranted, so it is unreasonable to ask anyone to credit such a claim.
So what about appeals to future technology, theories, and discoveries? Or to unknown spaces or alternate realities? Our guideline here should be that a proposal which requires a "perfect hypothetical" is ungrounded, hopelessly vague, mere thought. Because such notions have no connection with known reality, claims about them relative to reality are nonsensical.
For example, if I propose that a thing which is neither energy nor matter, and which contains none of either, will at some future time come to exist in an alternate reality beyond our universe which cannot be described in terms of our physics -- is anyone obliged to declare that I might be describing something real?
At first blush, it seems that perhaps we are obliged. After all, we can't disprove such a thing.
But considering the matter more closely, it becomes apparent that no such obligation adheres. Why? Because in that barrage of verbiage, I have not described anything at all. It is a purely negative definition, a non-thing in a non-space at a non-time. The term "real" loses any and all meaning with reference to such a concept.
In order to be considered a candidate for potential existence, a thing must have at least a toe-hold in reality as we know it.
Now, I have a simple, but serious, request: All definitions are slippery. So please, let's not get into hair-splitting over this definition, unless the objection has a direct bearing on the OP which can be explained. Thanks.
-----------------
*Yes, I say "off of". I'm from the South. I also want to know where things "are at". We love prepositions down here. We use them like spice. We create glorious phrases like "He was way on up out ahead of everybody" and "Get on down from up on top of there." We also look "up under" the bed for things we've lost, and tell people to go "up under" the overpass when we give directions.