When photons, what make up radiation, have enough energy, they can spontaneously decay into a particle and an antiparticle. This is easily observed today, as gamma rays do this. It turns out that the photon is just one of a class of particles, called the bosons, that decay in this manner. Many of the bosons around just after the big bang were so energetic that they could decay into much more massive particles such as protons, and antiprotons. (SOURCE) That's where matter and antimatter come from. We know that antimatter exists because we have replicated it recently. (SOURCE) We know that the big bang at its earliest point (Not when it was a singularity, when it was just starting to expand. Were talking billionths of seconds here.) was an extremely dense and hot point with energy in the form of radiation, there was no matter. (Energy density is what makes the universe expand. And radiation played a prime role in the initial expansion.) Now where did the energy come from? We could be inside an infinite chain of universes called a multiverse and our universe could be the other end of another universes' black hole. Of course, that is all pseudoscience with no visual evidence. But it's nonetheless an interesting theory. We need to understand how singularities actually work before we can really dig deep into the big bang. You can never get to the point of when it was a singularity, a singularity signals the breakdown of general relativity, that point in time does not exist. So its probably going to be a very long while before we can have some solid evidence of what these singularities actually are. The best we can do at this point is try to fit them into mathematical equations and simulate them in super computers.