Notes

Atheism does not define how you believe the universe started, nor does it require you to believe that it started in a certain, specific way.  Atheism is strictly a way to describe a lack of belief in God or religion.  Hence, any explanation of a universe coming into existence without God is a viable belief for an atheist.

For the sake of giving you an answer which you might deem satisfactory: A singularity inside a black hole in a parallel universe exploded and caused the big bang, which brought an infinite amount of hydrogen atoms, dark matter and dark energy into existence and created the space-time fabric of the cosmos.  Gravity caused billions of hydrogen atoms to clump together and over time the centers of these clumps became hot enough to fuse the hydrogen atoms to form helium, and tada, your first stars were born.  As time progressed, some of these stars exploded and created additional elements including nitrogen, carbon, oxygen and sulfur, otherwise known as the bulk elements which most organisms on our planet comprise of plus sodium, magnesium, potassium, calcium, chlorine, and phosphorus. As the atoms of these clumped together (again through the forces of gravity), it allowed entities other than stars to form, i.e. planets, comets, asteroids and other forms of matter. 

Five billion years ago, through this very same process, in the outer-mid bracket of our galaxy, our Sun formed.  The leftover debris created our planets, and it still might be creating another one as we speak (I do think that one day the asteroid belt between Mars and Jupiter will clump together another rocky planet, but then again, what do I know?).  Earth formed, it cooled, another planet hit us, created the moon.  You should check out how close the moon was to us billions of years ago, it covered a lot more of the night sky!  Anyways (sorry I get ahead of myself sometimes because this stuff amazes the shit out of me), as the moon reached a certain distance, the Earth's rotation and orbit stabilized.  Due to its distance from its parent star the Sun, hydrogen and oxygen atoms mixed together and formed water, and the water was allowed to flow in the state of a liquid, and that my curious friend allowed life to form, develop and thrive.  Some say the water came from a comet, but if you want to know the truth about that, you're gonna have to ask another question on Quora.

Single cell, stationary organisms developed at the bottom of the oceans, and through time, became multi-celled and had the ability to move.  Eventually through generations of natural selection (that is a component of Evolution, if you do not believe in that you need to ask yet another question up in here homie), they became more complex and became capable of surviving outside of their aqua-environment, chilled out on land for for a few billion years while developing into millions of different species and finally around a few million years ago, one branch of those species evolved into early primates. Your 'human body form' is attributed to, well, you know, those damn apes.

Then, this is important, the apes, through some divine intervention figured out that all of the above is bullshit, created Adam and Eve, and told Eve not to eat an apple.  Afterwards the told Adam that the stick goes in the hole and a few thousand years later, you are reading this on your computer.