Let me jump in on this one, since I've got a decent background with astrophysics.
The leading hypothesis behind the Big Bang Theory at the moment is one that involves quantum particles and empty space. So, let's say we've got nothing. Absolutely, nothing. No space-time, no matter, nothing. But what we do have is Heisenberg's Uncertainty Principle, the Brooker-Dewitt Equation, and well, physics. Many quantum particles are in a state of superimposition, simultaneously existing and not existing, using the Uncertainty Principle, this allows for empty space to come into existence through sheer probability thanks to these fluctuations going on in a false vacuum. Once a particle, that is infinitely small as it's completely described by its radius that is/contains a true vacuum pops itself into existence, it can then expand exponentially resulting in the universe we have now. The math isn't all the way there, but at the moment it is definitely the closest we have to solving the "something from nothing" issue. The biggest issue at the moment comes from determining whether the laws of physics were created with the universe, or simply exist.