Why do you think physicists are having such a hard time describing, explaining, or even imagining what happened microseconds after the big bang?.. or even what happened before it?
Because it is difficult to recreate the conditions of a big bang in a lab, and the energy scales are very high and because they lack the mathematical methods to accurately calculate QCD predictions.
And because big bang is formulated as a singularity, and there is no way to know, how the laws of physics behave at a singularity.
The laws of physics as we know them now were shaped during and right after that crazy event - I don't see what's so magical about it.
If you want to calculate anything about big bang, you have to use the current laws of physics (albeit at quite different conditions). If you say the laws of physics were different then, there is no way to know, what they actually were. Thus no calculations, predictions or test can be made and you have left the realm of science.
That the laws of physics were invariant is the assumption that makes any scientific investigation of big bang possible. If they were changing all the time, there would be no way to know what actually happened, so there would be no predictive power of that explanation at all, just like a "It was magic" explanation.
Once you postulate evolving laws of physics, you have left science and entered metaphysics and philosophy.
edit:
It is well accepted by most physicists that all the forces (gravity, electromagnetic, nuclear, etc.) were shaped by events during cosmic inflation. I believe the most widely accepted theory is that all the forces were unified in some way, and were split apart during inflation. Such profound changes to the way the Universe operates changes all sorts of "laws" of physics.
You misunderstood the concept of unifying the forces. There was no difference between the laws of physics of then and now. The forces are still unified, but the usual energy scales are not high enough, so that we don't notice the unification, because of the broken symmetry at low energy scales. The assumption is, that if we get to the same energy levels as in the big bang, there would be no difference. That is the whole point of experiments like ALICE at the LHC.