Physicist: That right there is one of the great unsolved questions. Every experiment that’s ever been done (on this subject) verifies the conservation of mass and energy. While the amount of mass or the amount of energy may change (they can be interchanged), the sum of the two is absolutely invariant.
This naturally leads to the question above. There are plenty of theories bouncing around, but without a couple more big bangs to do tests on, it’s unlikely we’ll ever know for sure. As we learn, many of the theories will be ruled out, but we’ll probably never be for sure sure. Here are some examples that almost certainly won’t pan out:
Spectacular Uncertainty: Energy and time cannot both be exactly known. Over any time scale there is always a little energy error, but the larger the time scale the smaller the energy error. Generally, this takes the form of one or two extra particles that last effectively no time. For example; gluons (the carrier of the nuclear strong force) usually don’t even exist long enough to cross an atomic nucleus at the speed of light. But maybe, just maybe, the unimaginable amount of matter in the universe is some kind of amazing quantum clerical error. You could tie in the anthropic principle (if there weren’t lots of matter there would be no one around to see it, so since we can see it…) if you want, but still. That shouldn’t explain there being any more matter than the absolute minimum amount needed to have observers.
It is what it is: Maybe mass/energy conservation only works for T>0, but doesn’t mean bupkis for T=0. In other words, there’s an unexplainable asterisk on the law.
God/Goddess/Gods/Higher Power: Sure.
All this has happened before, and all this will happen again: Maybe the big bang wasn’t the beginning, but in fact the universe just goes through expansion, collapse, and re-expansion cycles. This has the advantage of explaining the big bang, and also eliminates the question about conservation of mass/energy, but it does leave lots of other questions. Maybe worse questions. Also, the universe gives every sign of wanting to expand forever, making it less likely that a previous iteration would have collapsed.
Bubbles: It could be that our universe “bubbled” off of an even larger universe, that had plenty of mass and energy to spare. This theory don’t answer the question, but it does push it back far enough that it’s hopeless to try and answer rigorously.
Keep in mind that none of these theories are technically scientific. Scientific knowledge is nothing more than what we can learn from observation, inference, and experiment. Beyond inference, we’ve got very little to work with as far as the big bang goes.