Interesting that humans need to have all the answers. Why can't we accept some unknowns? Not saying, I'm any different, though.

For me this is an ultimate question of, whether you believe in god, God, other deity or in science. In the first case, the reason for universe's existence is self-explanatory, it is that deity responsible for it. As to why, it is impossible to know for us. An ant cannot and will not understand humans, and so we cannot hope to know the intentions of the being capable of creating universe. Since there was no communication (or you can believe there was, and accept religion) we must accept uncertainty.

On the other hand, if you reject existence of all-powerful, all-knowing being, you end up with Science. And Science bases on proofs and facts. But not much is really known about big bang. This is just a leading theory, but I think that nowadays, scientists tend to say we live in multiverse, where we are but one of infinite number of possible universes. But why does this multiverse exist? Seems to me like this is just adding another step on the ladder.

Long time ago, people believed that there was just one continent. Then, they discovered others. After that, they discovered another planets, another galaxies, local groups, clusters of galaxies, superclusters, and finally we ended up with observable universe. But that is just the limit of our current technology. As we see, historically with the invention of new technologies, we increased the size of our "universe". What I want to say is that, we cannot hope for Science to give us all the answers.

To sum up, the way I see it, we must accept the uncertainty. But that does not mean we have to stop looking for an answer. You can also do a further reading on Pascal's wager. I am not convinced by it, but it can give you an alternative solution to your question.