Salaamun Alaykum
 

I'd like to tackle this question from a non-legalistic perspective, but rather from a rational perspective. 
There are certain things that we are not able to grasp. Look for example at the 1st sermon recorded in Nahjul Balaghah:
Praise is due to Allah whose worth cannot be described by speakers, whose bounties cannot be counted by calculators and whose claim (to obedience) cannot be satisfied by those who attempt to do so, whom the height of intellectual courage cannot appreciate, and the divings of understanding cannot reach; He for whose description no limit has been laid down, no eulogy exists, no time is ordained and no duration is fixed. He brought forth creation through His Omnipotence, dispersed winds through His Compassion, and made firm the shaking earth with rocks. 

Look especially at these lines:
whom the height of intellectual courage cannot appreciate, and the divings of understanding cannot reach;
 

Imam Ali (pbuh) says that God is such that he cannot be fathomed by our limited understanding. In my humble understanding, this would also cover your query, i.e. why does God exist. 

Now think about from a different perspective - what would exist if there was no God? Such a question cannot yield anything but utter confusion, for in our understanding of existence, there is no existence except by God.

Although we would normally not reply to a question by saying "just accept it", this I would say is such a question.

With Salaams