So when the atheist says "prove it" and the Christian can't, the atheist claims victory; and when the atheist says "I don't know" the Christian claims victory.
I don't think it's as simple as that.
All of us begin with our respective axiomatic presuppositions. For example, you assume that yours is reasonable because it follow certain rules of logic, but when anyone would ask you to "prove" that the foundation for the rules of logic is valid, the only thing you can do is to either point to some pluralistic consensus, or some axiomatic necessity.
Thus, it's not the case of a Christian must prove something to you based on your philosophic model of reality. You first need to justify your model of reality in order for any side to accept that what you would consider "invalid evidence" is actually a viable conclusion.
Your model is based on "first principle" assumptions that you can't justify or provide "proof" for.
What we essentially have is two varying models that are built using different presuppositional philosophical frameworks.
The Christian position seems to be this: God created the universe (and also other realms beyond the universe) out of nothing by speaking such things into existence. I do not know of any explanation that is more specific than this.
There is not single "Christian position", just like there is no single and unified "atheist position" on this topic. The default position is "we don't know". That's why it's called a belief in God, instead of a claim of knowledge. A belief is a guess based on certain claims and lines of evidence.
Now, the debate is not about logical viability, because we first have to agree about rules of logic and context you are framing these in. You seem to be citing fallacies as though these are some sort of universal judicial decisions. These are not. Fallacy claims are not absolute. These are contextual, and only work within certain observable and repeatable variable context.
Saying that God created "something out of nothing" is a linguistic attempt to describe reality. Language is by necessity axiomatic. It's not absolute. It's not 1:1 representation of reality. It's just collection of symbols with send to communicate meaning.
Thus, when a Christian says something, there's a different semantics involved than when a scientist says something, just like when a philosopher says something, there's a different semantic meaning to the similar words that we speak. We may use the same words, but these words may not map to the same concepts.
Each of us gives individual meaning to the words.
The word "nothing" could have a wide range of meaning in this context, and it's highly unlikely that it's "abstract nothingness" that you are talking about. We don't know.
The point of that statement is not about HOW God created, but THAT God created, and it's a presupposition based on certain line of observable evidence.
The problems with this assessment are, first, that the Christian tacitly asserts that God exists for no reason and with no cause, which is the special pleading fallacy. Identifying the fallacy is already sufficient grounds to ignore the rebuttal until it is amended, but it can also be said that the second objection is inadequate.
Again, your referring to reason and cause here is problematic. You have to axiomatically presuppose the viability of both for us to have this conversation.
If you watch West World, they are making a hidden statement about it in the show intro animation. Robotic hands are playing the piano, and it looks like the robot is causing the piano to play. But then robot removes the hands, and the piano keeps on playing on its own. So, what we assumed to be a causal relationship turns out to be not causal at all. Piano and hands just move together to make it look like so.
Thus, you assume causality, because you perceive something simultaneously happening. But there's no conclusive means to prove causality. It's an assumption that your brain seems to connect based on patterns, and we can agree on certain causal relationships, but we don't need to agree that everything is causal and everything plays by the same causal rules. It's your assumption, and perhaps we can all agree to assume something, but that agreement is pragmatic and not based on some ontological validity.
The same with reason. You are assuming that there MUST BE a reason for everything that exists from your assumption about causality. But it's a foundational model that you formulate and you have to justify it. And I can assure you that you can only justify it so far before you run into the very same logical fallacies that you seem to think must be valid in any context.
We have not, and presumably cannot, observe nothingness, so there are no empirical grounds to say what can or cannot occur. Further, we know that nothingness entails a complete lack of rules or governing principles, so the governing principle "something cannot come from nothing" cannot apply to nothingness by definition.
Well, how do we know that nothingness entails and what it does not entail? Nothingness is a word that refers to absence, and we have to agree on your own subjective meaning of that word prior to us using it.
You may point to dictionary for some proof of words meaning, but linguistic meaning is not a static phenomenon. The only "true" meaning of the word labels is that which one we can agree on in any particular instance we use it.
If you say "nothing" means X, and I say nothing means Y ... and we do so axiomatically, then there can be no further conversation. We simply talk past each other insisting that our axioms are valid.
However, this is not how causality works. An agent performing the causal influence is only half of what we would call an event that involves causality. There must also be a thing that is acted on; otherwise there is no effect. Billiard balls are often used as an example of causality, but a billiard ball flying through empty space devoid of interaction is not causing anything to occur. Another billiard ball is required for causality to have meaning because there is no cause without something that gets effected.
Again, you don't know how causality works in any given situation. You are making a baseline assumption that you don't seem needs to be defended.
1) You can make a good claim of contextual causality as a pragmatic axiomatic assumption. If we see something that consistently repeating as a causal result, then there's a good pragmatic necessity to assume that A caused B.
2) When you are talking about non-repeating, or extremely complex phenomenon, causality is very difficult to infer, or even presume at all.
In terms of the transcendent reality, we can only philosophically infer what it may be like using the language of our reality. That's why the term is "God created something from nothing". It's a loose metaphor, but the point of that metaphor is not a scientific explanation. It's a philosophical point that God is the "ultimate source". Is there a source beyond God? That would be another level of discussion.
Absent creation, when the sum total of all existence was just the Christian God, what was available for God to act upon? Did God act on himself? Then we are all made of the stuff of God, and I don't think Christians take this position. Did God act on the universe before the universe even existed? How does that make sense? Did God act on nothingness? Nothingness is not a thing that can be acted on, and "acting on nothingness" is the same as acting on nothing, which is the same as doing nothing, which is the same as not causing anything to occur. God himself, nothing, and the universe itself seem to be the only conceivable choices of what we can even discuss as candidates for what God acted on, and none of them work.
Again, you are attempting to evaluate God in context of your own semantic model in which it naturally doesn't fit. When you axiomatically define meaning of certain words, OF COURSE you basically define God out of possibility with these axioms.
You would have to first justify your model prior to us having this conversation on some viable grounds. If you can't, then what are we talking about here? Your presuppositions? Why would that be more valid than presuppositions of other people? Because it seems like so to you

?
It's because the Christian's explanation for the origin of the universe is necessarily worse. The Christian cannot account for God's existence (because God exists for no reason and with no cause), then insists that God is necessary for creation to occur, yet cannot explain, even given God's unlimited power, exactly why God is necessary for the process or what God did.
It's sort of like demanding to explain how can quantum entanglement do what it does? We don't know. At the level of "derivative concepts" we can only make only so many assumptions, because the model lacks data.
These assumptions exists on fringes of presumed causal relationships, and these don't and can't explain the reality behind these entities. These models are derivative to begin with. That's the FRINGE of our understanding. It's difficult to guess what's behind the guess, because there are no constrains for us to hold on to.
Again, it's a philosophical model. For you to claim that it's "worse" what are you comparing it to? You are comparing it to your own model, and I'm asking you to justify that model prior to having this discussion. It's sort of like jumping on physics forum and asking to justify the "Many Universes" explanation, or various explanations behind quantum phenomenon. We never observe either our Universe, or quantum phenomenon except in some derivative manner. We assume that these things are as we imagine these to be.
So the Christian has an extra assumption which explains nothing, and assumptions that explain nothing are supposed to be dropped.
Why would the "extra assumption" be inferior explanation as to "less assumptions". You first need to justify THAT ASSUMPTION that you are making here, and you need to show that it's valid in every context of its application before you rush in and apply to everything.