What do Atheist Believe?
That's easy, atheists believe that theists are wrong.
You're conflating atheist with critical thinker, which is understandable given that critical analysis of the evidence for and against god claims leads to agnostic atheism. Critical thinkers recognize that belief by faith - unjustified belief - is a logical error to be avoided.
I used to be an atheist. In retrospect I can see I believed in the unbelievable. Not wishing to light the blue touch paper for other atheists to start ranting but as an atheist I personally would babble endlessly to Christians in my family and anyone that tried to evangelise me that science had all the answers. Thankfully I’m an awakened born again Christian
If you babbled about atheism and science then, you likely babbling about gods and religion now. Being a babbler isn't related to belief.
It seems to me that Atheists are most concerned with proof.
You're in the same boat with the poster above. Critical thinkers are concerned with whether claims are supported by sound arguments, since that is their currency of belief.
does an atheist live life expecting everything to be explainable.... factual.... proven?
No, but a critical thinker, who will also be an empiricist, lives life according to what he does know, knowledge being the collection of demonstrably correct ideas - ideas that can be used to predict outcomes - one holds.
So your whole identity as a human being is to be an atheist?
That's very little of my identity, which is based more in who I am, how I feel about that person, what I have become and done and how I feel about that, how I decide what is true about the world, and what I believe - not what I don't believe.
I am actually wanting to get some ideas because I am interested to know if atheism is an experience of a general lack of belief.
Atheism isn't an experience. It's exactly analogous to avampirism and aleprechaunism, which are also expressions of unbelief due to insufficient evidence to justify belief, also not experiences, also nothing that would define a person, also agnostic positions meaning that the existence of vampires and leprechauns can neither be ruled in nor out and that therefore neither should be believed to exist.
I understand there is atheism and there is agnosticism. Agnosticism is what everyone experiences to certain degress, however, I am curious to know if atheism is possible in humans, and if so, how does it affect ones belief structure.
I am an agnostic atheist, the commonest kind.
So you are content with your proof in your belief system coming from stories or happening to other things or beings?
If he's a critical thinker, he is vigilant to ensure that none of his beliefs are arrived at that way. The faithful believe such stories.
It is hard because from my understanding Atheism is entirely weighted on rejecting claims made by people's beliefs, typically supported by an idea that there is no physical proof therefore impossible or unreasonable to believe in deities. What I am trying to see is if that same scrutiny is placed in all belief systems outside of deites?
Yes, it is. But please learn to say critical thinker rather than atheist. Astrologers can be atheists, but most atheists reject astrology, because most are critical thinkers, not because they're atheists.
What specific expectations are you looking for? Visitation? Miraculous unexplainable occurrences?
I'm not expecting anything from gods, nor from theists. I understand that no evidence that makes gods necessary or even more likely will ever be adduced in my lifetime, and expect that to be the case forever.
Why doesn't the Earth and its vast variety of species and intricacies meet your expectations, where it would most non-atheists?
Because the naturalistic (godless) alternative is more parsimonious, making it the preferred narrative. Gods won't be added before they are needed to account for some new finding requiring a supernatural intelligent designer. People ask what would fulfill that criterion. Answer: nothing can do that, so nothing ever will even if gods exist but don't modify nature in ways that nature could not on its own.
I would still prefer a naturalistic explanation - a race of superhuman, extraterrestrial, intelligent designers that arose naturalistically through abiogenesis and biological evolution, but with a big head start on man, because that answer is also more parsimonious than a theistic one. It only requires that things we know happen to happen, such as molecules coming together to arrange themselves into life and gene pools varying over time and being selected for by blind physical processes. We have all of that.
Atheist simply do not accept the Scriptures as evidence of testimony of God while theist would.
Critical thinkers don't accept any holy book as evidence of gods or the supernatural.
If atheists are still able to believe in something based on logic, and theism was born from making logical sense of this world, I personally don't see how atheism can operate cognitively.
Trying to make logical sense of the world doesn't mean success at it. Theism is not logical. It is faith-based. Logic gives us sound conclusions. There is no sound argument that concludes, "therefore, God," meaning that if you hold that belief, it is perforce by faith.