> It's always been my understanding that the normal laws of physics don't work at big bang time as well.
That's wrong. As soon as the universe's mass/energy expanded sufficiently for there to be a time dimension (IOW as soon as the universe was something other than a singularity), the present physical laws applied. Some of the physical constants with which we are familiar may have had different values, but the same set of rules have been in effect since there were four distinct dimensions. This is borne out by the existence and properties of the CMB, as well as other observations.
Your use of the term "big bang time" implies that there was, in fact, time, which means four dimensions existed, which means our present physical rules were in effect.
One idea has it that the natural forces we evaluate separately now, were unified by the conditions of the early universe, but this idea doesn't contradict the notion that basic physical principles were in any way different then.
One of the more interesting cosmological ideas is that the positive mass/energy of the universe is exactly balanced by negative gravitational potential energy, as the universe expands and continuing to the present, but only at one specific expansion velocity: what we call escape velocity. If this idea is true, it means the universe could have sprung into existence spontaneously, like a virtual particle pair, without violating the law of conservation of energy. Stephen Hawking explains this idea in his book "The Grand Design": "Because there is a law such as gravity, the universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God to light the blue touch paper and set the universe going."