I can't improve on Phil's answer, but let me present a slightly different perspective.
The name "Big Bang" originally referred to the time zero limit of the FLRW metric. Since Friedmann et al inflation and quantum gravity have muddied the waters, but let's stick with the FLRW description and ignore the complications.
If you make a few simplifying assumptions about the universe you can solve the field equation and obtain the FLRW metric. Once we have a metric we can examine the evolution of the universe with time, and in particular work backwards to time zero. If we follow time back to zero we find the curvature goes to infinity, and this happens in a finite proper time (13.7 billion years in fact). Since we can't do arithmetic with infinity we can't integrate further back to times less than zero, so it's commonly said that time started at the Big Bang. Hence your confusion about what preceded it, and your statement:
Before that there was no time, no laws, nothing.
But actually you can't make the above statement. All that can be said for certain is that GR has no way of describing what happened before the Big Bang. This is quite different to the statement that there was nothing before the Big Bang because we know GR can only be an approximate theory at very small distances and very high curvatures.
As Phil mentioned, it's widely believed that near (apparent) singularities we can only get a good description of the physics by using some theory of quantum gravity. We expect this will allow trajectories to be calculated back through the Big Bang to times preceding it. The proponents of Loop Quantum Cosmology already claim they can describe what happens at the Big Bang, and they find it's actually a Big Bounce and the singularity never forms. However these calculations are far from universally accepted. I believe some proponents of String Cosmology have also claimed to predict a bounce, but I don't know a lot about this area and I believe the claims are rather speculative.