The question posed; How Do We Exist?
That's certainly debatable as there's more than one theory of cosmological evolution.
Big Bang Theory has stood up to scrutiny quite well but maybe the phrase "according to Hoyle" will someday make a comeback with the Cyclic Theory.
Then there's simulated reality to consider.
See:
http://en.wikipedia.org/wiki/Simulated_reality
Bostrom's Simulation postulated that we don't actually physically exist but that our perceived consciousness & the universe in which we're led to believe we exist within is merely the result of clever computer programming. What are the odds that we're all nothing more than code within a program & that program was created to entertain the rug-rats of higher beings?
See this brief review.
http://www.stanford.edu/class/symbsys205/BostromReview.html
When I was a preteen I had an experience that caused me to question whether life as I'd perceived it was real or something else. That kinda blew my socks off, had me conjuring up ideas of what life might really be. Some years later I learned of Simulated Reality & I wasn't so quick as others to dismiss the probability.
I don't think the question of How Do We Exist is very important within the grand scheme of things until we can answer Why We Exist.