Hi Carolyn,
Wheelers question ''How does something arise from nothing? '' seems to express amazement that something exists indeed. However, if the most fundamental, most obvious law of all of physics is the conservation law which says that what comes out of nothing must add to nothing, then there doesn't exist anything at all. Indeed, if in a universe which creates itself out of nothing, without any outside interference everything inside of it has to add to nil, to cancel, including space and time, then the universe is that unique, paradoxical 'thing' which doesn't exist, has no physical reality as 'seen' from without, but only exist as seen from within, to an observer the particles of his body being part of the sum which is to remain nil.
If the universe would contain only a single charged particle (among uncharged particles) so it wouldn't be able to express its charge, then it cannot be charged itself. If charge, if any property lives within interactions between particles, if particle express and preserve their properties by interacting, by exchanging information, then 'its', particles, particle properties are as much the cause as the effect of their interactions, of forces between them.
If the information as embodied in particle properties and the associated rules of behavior aka laws of physics in a self-creating universe must be the product of a trial-and-error evolution, then information only can survive, become actual information when molded into physical, material particle and tested in actual particle interactions: only that information survives which enables its carriers, readers/writers to survive. If the universe would contain only a single charged particle (among many uncharged particles) so it wouldn't be able to express its charge, then it cannot be charged itself. If charge, if any property lives within interactions between particles, if particle express and preserve their properties by interacting, by exchanging information, then 'its', particles, particle properties are as much the cause as the effect of their interactions, of forces between them. If particles only exist to each other if and for as long as they interact, exchange information, then you cannot have one without the other, nor can one be more fundamental than the other, causally precede the other.
If a particle cannot exist, have properties if there's nothing outside of it to interact with, then the same must hold for the universe. The fallacy of big bang cosmology is that we can only speak about the properties and state of the universe if there's something outside of it the universe can interact with, something it owes its properties to, that is: if it has been created by some outside intervention. For this reason big bang cosmology is an even worse 'theory' than creationism which at least honestly, boldly states that, yes, there is Someone outside of it Who created the universe. (And no, observations which seem to indicate that we do live in a big bang universe are less unequivocal than presently is assumed.)
Your second axiom, that space is quantized, made up of discrete units, is formulated from an imaginary observation post outside the universe, which is scientifically illegitimate: the meter and second are not defined outside the universe. Though energy is quantified, that does not mean that the Planck constant is a minimum energy quantity, and hence the Planck length the smallest possible length in the universe. If in blackbody radiation there are more energy levels per unit energy interval at higher energies, temperatures, so we need more and more decimals to distinguish successive energy levels at higher and higher energies, then the energy gap between subsequence levels can become arbitrarily small. Though energy is quantified, there is no minimum limit to the size of the quantum, so the Planck length and Planck time etc. have no special significance. The Planck constant h is like the number 1 in mathematics, encompassing all values between 0.5 and 1.5, so if we can measure the Planck constant in more decimals, at higher energies, then we can write that number as 1.0, which encompasses all numbers between 0.95 and 1.05. So if in our equations we set h = 1, then every time we improve the accuracy of the Planck constant, we increase the magnifying power of our microscope with a factor 10. In other words, the extent to which spacetime is defined, detailed somewhere, depends on the local energy density, so space is not built from discrete units which have the same size everywhere. To make matters worse, the observed energy density or definiteness of an area of spacetime also depends on the mass of the observing particle, the distance its 'looks' from and its motion.
Regards, Anton