It is too general to say that all atheists believe God does not exist
Agreed, but I would modify that to most atheists do not claim that gods (what you've called God) cannot or do not exist.
However there is semantics in the idea that atheism is no more than a lack of belief and many atheists fight tooth and nail against the idea that they believe anything, as if what is called religious belief (as opposed to scientific belief) is a dirty word even if many theists have come to their belief using reason and evidence.
I'm an atheist, and I make no such claim. I have countless beliefs. It's just that none derive from unbelief in gods. If this is hard to see, imagine somebody who does not believe in vampires. Which of his other beliefs derive from that one?
I still don't understand why this is an issue for the Christian apologist. What point is he trying to make? What's your purpose for making the point that atheism is a belief? I disagree, but even if I agreed, why would that matter to any apologist?
With many atheists it seems to be a matter of not wanting to explain their position and wanting to put a burden of proof onto the theists to show what they call suitable and enough evidence to convince them.
In my experience, every atheist on these threads is happy to explain his beliefs to any theist. And yes, if you want to convince an empiricist of anything, you'll need compelling evidence.
But of course there is no burden of proof on a theist to do anything of the sort.
There is no burden of proof ever unless two conditions arise: he wants to be believed and he is dealing with somebody who is willing and able to evaluate an argument for soundness and be convinced by a compelling argument. I make declarative statements at times that I decline to support, such as a recent one that Trump was very vulnerable to criminal indictment. I was asked why I believed that. I told him that he has had access to all of the same evidence that the rest of us have had, and if he doesn't see criminality there yet, he never will, and that therefore it was futile for me to present it again. One has no burden of proof with a person who cannot evaluate evidence properly, nor when one isn't interested in changing minds that perhaps could be changed. Not only do I believe that I could not change your mind about gods, but I would also not make you an atheist if I had the power to do so. I have neither the ability nor the desire to do that, so neither condition obtains in that case, so there is no burden of proof here for me.
The truth is that the evidence is there for all to see if they want to and that some believe the evidence points to the existence of God and others believe the evidence does not point that way.
Evaluating evidence isn't as subjective an enterprise as you suggest. The evidence believers offer for God is not evidence for any god over naturalistic alternatives according to rules of interpreting evidence in critical analysis. To say it is is to misunderstand what that evidence implies about reality. Reality is evidence that reality exists, not that a god was required. That is merely one of two logical possibilities, the one that violates Occam's principle of parsimony.
I would say that there are beliefs that do come from this sort of atheism. One would be a belief that life is no more than chemistry and physics.
The agnostic atheist says that life may have originated naturalistically. One shouldn't need to be an atheist to believe that. One can believe that that is not how it happened, but that there is no evidence to rule it out, either. And one need not be a theist to believe that life might have been intelligently designed. This is pure reason - two logical possibilities exist, neither of which can be ruled in or out at this time.
Incidentally, life is also biology and ecology, higher order emergent sciences. They are powered by chemistry just as chemistry is powered by physics, but contain emergent phenomena like biological evolution not found in nonliving matter. One wouldn't say that Shakespeare is no more than typographical characters (letters, punctuation, spaces, capitalization). When we combine these, words emerge, which carry more meaning than letters. When we combine words, sentences emerge, which carry more meaning than words. And when we combine sentences, poetry and stories emerge. That's emergence - phenomena observed at some scales but not others. No water molecule is wet. Wetness emerges from collections of liquid water.
all life that we know comes from pre-existing life.
You don't believe that, and neither do I. Wasn't it you and I that just went through this? Maybe it was another poster. Whether you call a disembodied mind like a deity living or not, there exists a first life form not derived from other life. Is God alive to you? Then that is life that didn't come from preexisting life. Is God not a living thing to you, because you use a scientific definition of life that includes growth, repair, cells, reproduction, metabolism, etc. as criteria for life? OK. Then the life it created is life coming from nonlife.