Atheist = lack of belief in God/gods.
It absolutely is that simple.
Here's a question. Why do you insist on this "careful consideration" clause for belief in God when you wouldn't insist on it with any other thing in life?
If you're not wet, you're dry. You don't have to sit around and ponder if you're wet, or make a conscious decision and say "after further review, I am not wet, therefore I am dry."
It's just as simple as not being wet = being dry. The same is true with atheism. Not being a theist = being an atheist.
No one tries to place this idea of "you have to go through careful consideration of the issue" on any other aspect of life. Someone who has no natural sexual urges is asexual...they may never have even heard of that term, but they are it. They don't have to sit and ponder or consider, it's just the sexual urge is absent in them so they are asexual.
You must try to understand that the only reason you're insisting on this idea that atheists MUST put long, hard thought into the issue, is because the belief in God is so deeply ingrained in you personally, that it's hard to imagine others having the absence of it without any thought at all. But it's entirely possible and the term atheist applies to those people as well as atheists who may have put thought into the matter.