Strong QO is the notion that quanta can produce things which are not composed of quanta, such as space-time. That in itself involves a gap, as we have no idea how that may happen. It is a gap, not a paradox, because there is no suggestion of contradiction (as yet). It is complex, because the explanation must account for diverse phenomena which interact with each other in various ways. That gives it an Occam score of 0300.
Strong QO accounts for natural law, in exactly the same way as QO does. All that is, emanates from original quantum.
Strong QO accounts for a finite big bang, as follows. Matter can only exist if the total gravitational energy exactly matches the total energy associated with particles (including particle energy, kinetic energy, and whatever other energy particles may have). Given quantum mechanical processes, sooner or later (probably very much later) there will be a quantum fluctuation that fits the bill. This will have to be very massive in order for the gravitational energy, which is proportional according to the square of the mass, to balance the particle energy, which is proportion to the mass. Once this happens, space will immediately contract, a behaviour popularly known as a Big Crunch. Once space cannot contract any further, space will start expanding again, producing the Big Bang.
Strong QO is in any event preferable to the explanations provided by mainstream science, because they each have the same issues in accounting for the non-quantum phenomena, and do worse in accounting for natural law.