Recall my first post to this thread. Let's take an alternate topic and ask the same question. Suppose, that instead of asking about God, I were to ask the question "What is the evidence that the sun is real?" Or, in terms of my opening post "I invite our resident Sun-believers to put forward what you regard as the best evidence for the existence of this 'Sun' that you believe in."
It occurs to me that, immediately, it would be possible to point to lots of suggestive evidence. For instance, there appears to be a big bright thing in the sky when you go outside, at least some of the time. That bright thing is demonstrably associated with heat and light. When the bright thing isn't there, the heat and light are both diminished.
Of course, even to ask the question, we must have some shared idea of what the word "Sun" means in the first place. In a very real sense, that big bright thing in the sky is the Sun by definition.
Application: I think that atheists and theists have some shared idea of what the word "God" means. Would the theists here argue that God is therefore real by definition? If so, what, exactly does the term "God" refer to? And what is the shared frame of reference that atheists and theists agree on in order to recognise the reality of the thing defined in that case?
---
One way to tell if this "Sun" is a real thing is to consider what things would look like if it was absent. The first thing to say about that is that you don't make the Sun absent simply by refusing to call it the Sun. You're evading the point if you say "There's no Sun. That big bright thing in the sky is the foozwimple, not any kind of sun-thing that you Sunists say exists." We both understand that what requires explanation in the context of the question that was asked is not the name we give to the apparent source of the heat and light, but whether such a source exists or does not exist.
So, the second (and third, and fourth) things the sun-believer will typically point to is that if the Sun did not exist (as described/defined), then the Earth would be cold and dark (for example), which is in stark contrast to what we all experience, Sun-believers and Sun-deniers alike.
Application: what would the universe/ourselves/the earth/life/anything look like if there was no God? Would it necessarily look any different? If the theists say it would, they need to explain what the necessary differences are. Note: it is not enough to assert that "If God did not exist, nothing would exist". I could make the same claim about the Sun: if the Sun did not exist, then nothing would exist, so therefore because something exists, the Sun exists. That doesn't work as an argument for the Sun, or anything else, including God.
---
On the matter of epistemology, we must have a certain shared frame of reference. In order to discuss the possibility of a Sun, we need to be able to agree in advance that warmth and light typically require a source, for example. We need to agree that heat and light themselves exist, independent of this postulated "Sun" thing we're debating. But these aren't big hurdles. It's not hard to reach agreement on experiences we all share.
Application: in contrast, it is not at all obvious that the universe as a whole requires a source, and in particular, it is not at all obvious that a source fitting typical descriptions of "God" is required.
---
We could ask a more complex question, of course. For example, I could ask "What's your best evidence that the Sun is a star?". Or I could ask "What's your best evidence that the Sun is made mainly of hydrogen?" You might need to have some specialist knowledge to know what constitutes good evidence of either of those things, and I might need some specialist knowledge to be able to evaluate the evidence you put forward.
But notice this: even if I might lack the expertise to fully evaluate your evidence, it is not a pre-requisite that I share your belief in order for your evidence to even make sense. It's not a valid response to my question for you to say "Only somebody who already believes the Sun is made from hydrogen is qualified to understand any evidence I might put forward for that claim. And the fact you're even asking the question proves that you're an evil Sun-is-hydrogen denier, so that tells me that presenting the evidence would be a pointless exercise. Why don't you go off and google some sacred sun-is-hydrogen texts? Come back and talk to me again once you believe that the Sun is hydrogen. Until then, I refuse to point you to any evidence."
Application: Jan Ardena's and Musika's refusal to provide any evidence of God on the grounds that atheists would first need to believe in God in order to appreciate the evidence is empty. If suitable evidence exists, then its validity as such must be recognisable independent of the particular conclusion that it is supposed to support. This is what it means for something to be evidence of something else.
To expand a little on that: I don't need to have a pre-formed belief in stars or Suns to accept the methods for identification of hydrogen. And this in fact strengthens the value of hydrogen as evidence of the Sun's composition. I don't have to start by believing that the Sun is made of hydrogen. I can check for hydrogen in the Sun independently of any prior belief I might have about the Sun's composition.
Question to theists: is there any way I can check for the existence of God that is independent of my prior belief on that question?
---
Final note: it is, in general, possible for a person to go from a state of non-acceptance of something to acceptance, based on evidence. For instance, if I say "The Sun is made of hydrogen" and you start from "I don't believe you" or "I'm not convinced about that", then by presenting appropriate evidence I can change your mind, in principle. I can convince you. It is true that some effort might be necessary on your part. For instance, you might not know how hydrogen is recognised, but in principle I can explain that, or you can find out for yourself from other sources. One additional important point here is that you don't ultimately have to accept any complicated argument based on authority to identify hydrogen (say). Provided you are willing to buy into some generally accepted definitions of words (which is necessary to ensure we're both talking about the same thing), you can in principle check for yourself whether each step in the evidence/reasoning process that leads to the conclusion (in this case that the Sun is made of hydrogen) is true or false. There is no sacred Sun-is-hydrogen text that you must accept as an authority at the beginning of your inquiry.
Caveat: you can't simply define something into existence, other than as a concept or idea. It's not enough for me to say "I define the Sun as a big ball of hydrogen in the sky." My saying that doesn't make the Sun exist in reality; it only makes the concept of a Sun exist in your mind. I haven't created a Sun merely by defining a word; at best I have created an idea. When we talk about evidence what we're doing is checking whether our ideas correspond to an observed reality. The idea of a Sun is all well and good, but if we all lived in a deep dark cave all our lives we'd have no idea whether the idea had any connection to anything real. No matter how many stories or sacred texts we had mentioning this "Sun", there would be no way to tell from inside the cave whether it was a real thing or just a fantasy*. To know whether it was real (as opposed to merely believing that it might be real) we'd have to venture outside the cave and collect some actual evidence.
---
* (To any pedantic physicists who might be reading: yes, yes, I know that in this particular example there would be ways, but you get the point of the analogy, I hope.)