I'm not even a scientist but I know several explanations for this that don't violate conservation of energy.
Quantum mechanics, is the main hypothesis right now, to explain how the Big Bang could have started. In quantum mechanics, as has already been scientifically shown, in a complete vacuum there is never truly "nothing." Constantly and randomly, empty space will, for an instant or two, spawn a particle and its anti-particle counterpart, which then combine and form "nothing," again. Picture, if you will, two flat lines at y=0 on a graph. Now, randomly, one line will go to y=3, and you'll see the other line go to y=-3. Both graphs (two y=0 and y=3,y=-3) equal zero, and quantum mechanics, for reasons unknown to us right now, does that exact thing. Why? Well, no idea, right now, much like not knowing *why* gravity exists, only that it does.
Anyway, so picture empty space. Absolutely empty. There will constantly be particles and anti-particles popping in and annihilating themselves almost instantly.
From there (it's really hard to explain the connection, as I don't fully understand it myself), we have a logical explanation for how the Big Bang could have occurred without violating conservation of energy.
I suppose the point of all of this is that "nothing" is NEVER EVER actually "nothing." It's always something, even if its net value is zero. Going from that, the net value of the universe is quite probably zero, even though we seem to live in a positive universe. Were the universe to collapse fully on itself, though, we would likely see that this whole expanse was one side of the particle-anti-particle-deal, with gravity and other forces being the opposing forces that cancel out the physical matter.
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