Why does the Universe even exist?

Well it's thought that most of the matter we have in the universe today did come from nothing. By nothing, I mean the vacuum. There is a favoured mechanism for creating the matter that fills our universe, and this is the convergence of the energy density of the vacuum. In simple terms, one would think of this as nothing, or no material, into matter. So in many ways, everything we see did come from nothing. The way energy density is converted into matter is quite complicated, but it's thought that that's how it occurred, through inflation.