The only well tested theory of gravity we have right now is general relativity (GR). In models based on GR, time and space only exist for $t>0$. In relativity, we use the term "event" to mean a certain position in space at a certain time. The big bang is not an event, because there is no time $t=0$. If you want to find a cause for some event happening at a given time $t>0$, there is always some earlier $t'$, with $0<t'<t$, that can supply that cause. Since the big bang isn't an event, it doesn't have a cause.
We also have fundamental reasons to believe that GR lacks self-consistency under the very dense and hot conditions at $t \lesssim 10^{-43}$ s (known as the Planck time), because of quantum-mechanical effects. If we had a theory of quantum gravity that worked under those conditions, then it might turn out that the singularity at $t=0$ was not real, and events at $t>0$ could be explained in terms of causes at $t<0$. This is what seems to happen, for example, in loop quantum cosmology. However, nobody has a theory of quantum gravity that works and has been tested against experiment, so we don't really know.
"I remember reading long ago somewhere that according to one theory time began shortly before the creation of the universe." I don't think there is any professionally researched scientific theory that says this. Theories that have time before the Big Bang generally do not have a beginning to time at all.