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I've read no good arguments against "How does something come from nothing". Every response I've seen involves a supernatural explanation.
Of course there isn't. That's why it's called faith. >

Well, some religious practitioners dispute that this is the meaning of faith. Many Christians, for example, claim that faith is trust based on the evidence. For example, the Christian philosopher John DePoe (who I respect a lot) wrote:

One final objection to Classical Evidentialism that I wish to address is that religious faith by its nature is opposed to evidence. What I am requiring of religious beliefs, some might say, is like asking oil and water to mix. Knowledge acquired through evidential arguments, they claim, cannot be a matter of faith.  
At the heart of this objection is an assumption about the nature of faith, namely that faith is an act of belief without evidence or even against evidence. I reject this view of faith. Faith is better understood (at least in part) as the dispositional characteristic to trust and persevere in one’s religious beliefs. Faith is a virtue that allows believers to remain steadfast in their religious beliefs because they have good reason to do so. (Debating Christian Religious Epistemology, p.27) >

There are circumstantial evidence, like the evidence of the existence of Jesus, David, the flood (probably on a smaller scale, but still significant), the plagues in Egypt and the genetic Eve (mithocondrial Eve) etc.
Do these things serve as an undisputable evidence of God as described in the Abrahamic religions? No, it only serves to show that the events described in the Torah, Bible and Qur'An have their roots in reality.
This means that there are believers ( there are a lot of believers, who simply have blind faith) who believe/have faith because of circumstantial evidences.
As said these are circumstantial evidences, however those can be powerful and a lot of scientific discoveries or legal judgements are based on circumstantial evidence (two good example would be the existence of black holes for the former or fingerprints and DNA tests in the latter). >

This feels a bit like saying that Spider Man is real because some of the events in the comics happened in New York and New York is real. >

No it's saying that the siege of Troy happened, because they found the ruins of the city. Now did it happen as described in the Illiad? Probably not. >

Right. So someone looks at the Illiad, finds evidence that the siege of Troy happened and concludes that Aphrodite actually exists. >

Well you can certanly think this way. 
I would say that someone finds the ruins of Troy, knows that kidnapping potential brides were a thing and also finds signs of an eartquake, if said person also knows that Poseidon wasn't only the god of the sea, but of earthquakes and that his sacred animal was the horse.
Based on these he/she goes to the conclusion that the Illiad was based on truth at least in the sense that the cause of the siege was likely real, the siege itself was likely real and probably the Troyan horse was real.
I would argue that the conclusion that the horse wasn't a trick, but a tribute to Poseidon for his intervention is logical. Also if said person has an inclination toward the spiritual side of life he/she might believe that the fall of Troy was due to divine intervention.
As I said in the last sentence, it's a belief, however one that has circumstantial evidence behind it. Is it true? Probably not, however it is a logical conclusion. >

Is it, though? Is it really a logical conclusion that Aphrodite exists because she's in the Illiad and we can verify that some of the things in the Illiad happened? >

Okay, first of all I didn't mention Aphrodite at all. Even the greeks didn't have a universal belief, just like modern religions doesn't have universal belief.
However, allow me to ask why the proposition I described would be illogical? >

I mentioned Aphrodite originally, because she does appear in the Illiad. I thought that you were addressing my comment, not some other thing.So it remains, if the fact that some mundane things in the Bible are reasonable evidence that God exists, then surely the fact that some mundane things in the Illiad being true are reasonable evidence that Aphrodite exists. >

Conclusive is a higher standard than we hold for practically anything. Science rarely, if ever, proclaims conclusive knowledge, almost always allowing for unobserved variable(s), evidence, data, etc. that would debunk current theories. We don't have conclusive evidence that consciousness exists, macro evolution has ever happened or we all didn't just come into existence a day or two ago in motion with a developed memory of life lived before. All opinions and beliefs on these and many other topics are based on a lower standard of belief than your CMV seems to expect of a deity existing.
Because of this, I ask - how is this view profitable to any discussions on these topics? How is conclusive a valid standard? I disagree with the implied validity of the observation you hold in your view.
Even in Christian teaching, Lucifer/Satan obviously didn't think the deity he interacted with was compellingly and conclusively all supreme, hence the attempt to usurp the Creator of the Universe. Even if you don't believe anything else in that worldview I would think we can all agree one individual's "conclusive" is the next individual's "not-even-compelling" and often that has less to do with the evidence than the framework from which the evidence is being evaluated.
All that to say-how can you be sure that your framework of expectations for what "conclusive evidence" a deity should provide would be considered valid and binding by any deity that may exist for such a deity to be just in judging you for rejecting the evidence they have given?
Personally, I find some intelligent design arguments quite compelling, especially around DNA's similarity to programming and the structure and design that implies. I think many scientists have failed to really evaluate some trends (frequency and in content) in near death experiences across cultures that suggest life after death is a more evidence based belief than not. I find some deists destressingly hypocritical and incoherent. But I find that true of some atheists and agnostics as well. I pray and study, and have had a number of experiences that wouldn't provide anyone else conclusive proof, but have affirmed over and over that there is a God who communicates with those who listen with their soul/spirit. I pray you'll come to know truth-whether it is what you want it to be or not. >

PART 1

Conclusive is a higher standard than we hold for practically anything. Science rarely, if ever, proclaims conclusive knowledge, almost always allowing for unobserved variable(s), evidence, data, etc.

I think that's a misunderstanding of what I mean by "conclusive." I don't mean it is undeniable, incorrigible, indubitable, unrevisable or absolute like proving a mathematical theorem. As I said, by conclusive I simply mean the "publicly accessible data makes the proposition significantly more likely than its contrary." In science, the data does usually make the hypothesis in question significantly more likely than its contrary. Similarly, that's the standard reasonable people use in real life when they have to make important decisions based on the data.

We don't have conclusive evidence that consciousness exists, macro evolution has ever happened or we all didn't just come into existence a day or two ago in motion with a developed memory of life lived before.

It is a category error to ask for empirical evidence of the existence of one's own consciousness. Consciousness isn't supposed to exist outside of our minds (like God or the external world). As Descartes pointed out, self-consciousness is the only thing that cannot be rationally denied, as one would have to affirm it in the act of denial -- since one is using it to know anything. It is a self-evident truth or a transcendental category, as Kant would put it.
Now, you chose the worst example possible to support your view, namely, a skeptical scenario regarding the past existence of the world. Even if we concede that there is no conclusive evidence the past happened (as our memory tells us), that is not relevant to anything; it is just an amusing philosophical problem. If one uses these skeptical scenarios as their standard of evidential evaluation, they may just as well believe that after we die, we'll be transported to a magical realm populated by beautiful fairies and dragons. No evidence? No problem! After all, you can't provide evidence the world wasn't created 5 minutes ago; you have blind faith in your memory!
With regards to the theory of Neo-Darwinian evolution, there is overwhelming empirical evidence that it is correct. Today that's virtually indisputable. >

Many deistic belief systems posit a deity outside our reality that has set in motion or ordered our reality, yet remains outside it. So I ask - how is it not a category error to ask for conclusive proof within the system of an entity outside the system of our reality?
Isn't that like a gold fish in a bowl saying the glass blower that made the bowl doesn't exist simply because they don't have proof? One can argue all day that the glass bowl is proof, but if the fish has convinced itself of another possible explanation that needs no glass blower an eternal skeptic they will be. After all it has observed how calcium and lime deposits build up on the glass bowl-so taken to it's logical extension, the bowl may likely have grown up over time in the same way. >

As you hinted in your analogy, the world itself could be the evidence of this designer deity -- so, it is not a category error. If it is indeed conclusive evidence, the fact that the pig-headed/closed-minded person refuses to evaluate the evidence rationally is no reason to think it is a category error.
I have a better example of a deity whose existence couldn't even in principle be evaluated empirically. Suppose a deity exists, but it did not create our world. In fact, it never even interacted with it -- and never will. Well, in this case, it would be a category error to ask for empirical evidence. But my definition of 'god' in OP already rules out this kind of deity. So, it is not really relevant to our discussion. >

In an infinite universe, all things are possible!