For example, if you believe that the universe was caused by a natural phenomenon called the big bang, its nature is a completely physical one, and that there is no purpose but the only guiding forces are evolution and other natural forces, then does that fit?
Atheism says nothing about this. Atheism is the lack of theism.
Do some atheist believe the above? Yes. Do most? Probably. But that is separate from atheism.
In your mind, is everyone that believes in a "big bang"(even though beginning of the universe is more complex than this term) and evolution an atheist.
There are a lot of theists that know those are real too.
Facts don't lie or have an agenda. Facts are just facts