Here is my concept of God: the unique uncreated creator and operator of the created universe.
The first problem I see with this sentence is that there are 2 descriptors for your concept of God which describe what it is NOT, and not what it actually is. To say something is unique is to say that it is NOT like other things. To say something is uncreated is to say that it is NOT created. It's like describing my computer as NOT a printer and NOT a toaster. We know what it's NOT; please try to describe what your concept of god IS.
Also, saying that God created and operates the universe is an unsupported assertion. It has not been established that the universe was created by a deity of some sort.
My personal feeling is that you need to try again.
And here is my concept of evidence: any fact man knows leading him to know another fact.
This is worse. I'd rather we stick with the standard definition of evidence here that you could find in most any dictionary. This is from Dictionary.com
1. that which tends to prove or disprove something; ground for belief; proof.
2. something that makes plain or clear; an indication or sign:
I do not accept your definition above. If you'd like to find or coin a new word to encompass what you said up there, feel free. But the phrase you posted does not define 'evidence'.
The certainty of God's existence or nonexistence must before everything else start with concurrence on the concept of God, otherwise folks i.e. everyone is talking past everyone's else head, and that is irrational behavior.
Now, since atheists insist on evidence, then specially atheists should work first to come to concurrence with theists on a common mutually accepted concept of what is evidence; otherwise everyone would be talking past everyone's head, which is irrational behavior.
We have one. We've always had one. There's been one for a long time. The problem is that theists tend not to follow the one in the dictionary and atheists do.
The problem is bigger than that though. God, for most believers is a foregone conclusion. They START by saying, 'There is a god' and work everything else back into it; whereas the atheist (most often) starts with the question 'Is there a god' and uses the evidence to guide that answer.
It also has a lot to do with how much of the evidence is actually taken into consideration. This concept has its roots in the sheer ignorance of all the available evidence.
For example: 'Jesus rose from the dead'. Now, the Christian will look at that phrase with the preconceived notion that God is real, so obviously, Jesus can rise from the dead. It's in the bible, and they take the bible to be 'evidence' that it actually happened. It ONLY works like this if you first believe in God. If you are an atheist, however, when you look at that phrase, you take it in a different direction. You see the bible as one source that confirms that Jesus rose from the dead, but you need more than that; so you look at who wrote the gospels (we don't know), you look at the historical evidence that Jesus rose from the dead (zero), and you look at how many of the original copies of the manuscripts we have (zero), and the 'evidence' that the bible presents suddenly gets pretty flimsy. Given the reality that people do NOT rise from the dead, and that there have been thousands of proposed gods or god like figures who have risen from the dead in the history of mankind, and that the odds that someone simply made that story up are so much greater than the odds of someone rising from the dead 3 days later, and it's a slam dunk.
You see what I mean? An atheist is guided by the evidence in terms of religious belief. On one hand, we have 'evidence' that Jesus rose from the dead in the form of the gospel stories. We also have 'evidence' (all that other stuff I mentioned, plus a whole lot more) that goes against that notion. When put side by side, the sum total of the 'evidence' here is massively against the notion that Jesus rose from the dead.
That's just one example; there are thousands you could come up with.
Coming up with a solid concept of what god IS is
a very good idea, however. Keep at it and see what you come up with. Don't beat yourself up, however, when you realize it's a completely nebulous concept which defies definition in any meaningful sense.