What is outside the universe? What was there before the Big Bang?
By definition, we don't know... Everything outside of the observable universe or before the big bang is outside the limit of our telescopes - by definition, and so there is no way anyone can make any measurement that could answer this question. Thus, lacking any real information, all we can do is speculate.
First, by definition of "universe", it contains everything. Thus, there is really no meaning to the question of "outside the universe". The origin of confusion is likely the following: We know that the universe expands. Thus, many people imagine that the universe expands into something - the same way as a balloon being inflated, expands into pre-existing space. However, the expansion of the universe is crucially different. The universe does not expand into anything; it can be infinite, and still expand - maybe easiest to think of it as "stretch", as the distance between any two points in it constantly increases with time, similar to rubber. Maybe a good analogy is a copy machine: if you would would take an infinitely big paper, and copy it using the zoom option, you increase the distance between every two points; if your original piece was infinitely big, so will the final piece be...
A different question is what lies outside the observable universe. Hubble told us that the universe expands, and therefore it has existed for only a finite time (the time since the big bang, roughly 13.8 billion years). Since the speed of light is finite, we can only observe light that has arrived to us from a distance of 13.8 billion light years; We havn't yet had the chance to observe light from more distant objects, since it has not arrived to us yet. (It may or may not arrive to us in the future; this depends of the rate of the universe expansion. If the universe expands too rapidly, we may never be able to see the light from some objects !). So what lies behind what we can see ?
The most simple answer would be "more of the same". This is suggested by the fact that the universe, on very large scale, look alike in all directions. This fact is not that easy to explain, given that the light from distant galaxies on one side never had the chance to reach distant galaxies on the other side. In order to explain this, it was proposed that at very early stages, the baby universe underwent a massive, very rapid "inflation". The theory - though difficult to prove or disprove - predicts that the universe is likely at least many orders of magnitude larger than what we can see.
For some further discussion, see
A somewhat similar question is: What was there before the big bang? Of course, the correct answer is that we have no way of telling. Einstein, for example, believed that there was nothing. One other idea is that before the big bang, there existed another universe, that collapsed... and from this collapse our universe emerged. But, really, your idea is as good as mine.