If matter cannot be created or destroyed how does one explain the outcome of the Big Bang?

The total mass, or total energy, of the closed system that is the Universe, is constant and has been constant since the beginning.

It is true that matter cannot be created or destroyed. We have to understand 2 laws, which are essentially the same. The conservation of mass states that in a closed system, during any reaction, total mass must be preserved, so the total mass of the reactants or the starting materials of the reaction will be the same as the mass of the products.

The adapted version for thermodynamics, which is the First Law of Thermodynamics, states that "The total energy of an isolated system is constant", so it may transform to other forms freely but cannot be created nor destroyed, it is a constant.

The Universe is an isolated system, and even with it being an expanding Universe, it means that at the beginning of the Universe, whatever form of Energy was present in the small point, after started, the , the energy present is the same as the energy present now. And mass is included in that too.

The Big Bang isn't an explosion in itself, it wasn't an explosion that created space, it was the beginning of an expansion which created space-time as we know it.