If you think about it, Steady State harmonizes with the concept of a God--a universe as timeless as the eternal supreme being who created it. Such is not the case with the Big Bang. If a beginning point in time has been established, the very existence of this point of origin for physical matter and energy means that there was nothing--not even space or time (an almost unimaginable concept) before the instant that the first particle flared into existence.
Obviously time is a measurable dimension and began at the instant that the universe popped into existence. One question that comes to mind (well mine anyway) is why did this event happen at the particular moment that it did, i. e. why 13 billion years ago? Why not 20 billion or 11 billion? In other words, why did God pick that particular time to start the ball rolling? What was he doing before then?
In addition there are so many contingencies after the birth of the universe that had to happen for physical matter to evolve and coalesce into galaxies which in turn are composed of stars one of which had the right characteristics to allow the formation of our planet. In turn, our world had to have just the right balance of chemical elements--and even a moon of the right size and distance for life as we know it to begin here. Then over eons, that life evolved from primordial soup to humans--and everything in between.
The intricacy of all these events is so staggering that (as Richard Dawkins points out in The God Delusion) for all this to have happened as the result of creation by a god who would have had to be even more complex than the universe and its laws does not make sense. One reason is the "first cause" conundrum. If God created the universe, who created God? It's not satisfactory to say that "he" has always been "there." Where was "there" if nothing existed prior Big Bang?
But back to the question as to why Big Bang occurred 13 billion years ago, for that matter why did it happen at all? Science has offered various conjectures. One of these is that Big Bang and the resulting formation of our universe was the result of a disturbance in a larger metaverse, and there may be an infinite number of other universes in other dimensions that were born in a similar manner.
In the distant future Earth will eventually become uninhabitable as the sun follows the typical life cycle of other stars. The sun's heat and size will grow to the point that Earth will be obliterated. By that time, humankind (assuming that we have not annihilated ourselves in the meantime)--or whatever we will have evolved into-- will have likely colonized other star systems. But the problem is nothing lasts forever, and that includes the cosmos. According to cosmological predictions, eventually, the universe itself will also come to an end in one of two ways.
Since the time of the Big Bang, the universe has been expanding. Eventually, this expansion may reverse itself, and the universe will collapse in on itself in the "Big Crunch". There is even speculation that the Big Bang, expansion, and Big Crunch have happened in the distant past and will repeat themselves in a never ending cycle.
The other possible finale will be an endless expansion and dissolution of the cosmos into infinity as every galaxy pulls further apart from each other, unravels, and every star eventually dies out. So just as it had a beginning, the universe will at some point have an end. Thus the cosmos carries within it the seeds of its own destruction, either with a bang or a whimper. This leads to the question why would God create the universe only to ultimately destroy it?
Through experiments that simulate the Big Bang, cosmology is bringing us closer to understanding the details of how universe began. But will it ever be able to explain the reason that out of what had been eternal nothingness, in a split second came the the beginning of everything that ever has been or ever will exist?
For a more expansive and articulate discussion than I could ever present on the questions raised in this post, I recommend the book Fabric of the Cosmos by Brian Greene.