erm , it seems that there are no current hypotheses as to this . A singularity to me is a position in space with no size and indeterminate properties . in this special case , it encompasses the universe we are present in .
1. The universe is observed to be of non-zero size and therefore not a singularity.
yes , crazy .... as I said ... we can see it isnt as you rightly say. Current mainstream physics suggest that space consists of matter being created/destroyed in a maelstrom via positive/negative units. my thoughts are that sometimes they survive long enough , the negative units having negative gravity , they are sprung apart and create 2 equal oand opposite quantum particles which have universal dimensions which are greater than the actual size of the particles , one negative 'size' the other positive 'size' . The terminology doesnt seem to exist in english [ it gets MUCH worse when talking about the time dimension] . thus the size of the universe remains the same , which is effectively zero , although there are local variations which is where we can observe . The negative parts of the universe being at the edge of the universe . If true try thinking of where the 2 volumes start to interact ..
2. The big bang describes the expansion of the universe so, again, it cannot be of zero size.
Granted . This hypothesis requires a universe equal to a diameter of a minimum of 2 fundamental particles to be produced to start and is its weak point . However if you accept that is more possible than other theories [ a darn sight less than the entire universe starts as a blip ? ] . Take the instant of creation : just before that point time was zero,in fact everything was zero . then 2 particles appeared and split . one has positive dimensions and time , the other negative. The universe has 2 quantum dimensions equal and opposite , and both will fly apart . time is VERY VERY slow , as this is literally the 'tick of the universe' . Imagine the entire universe flying apart , albeit just 2 particles into the space allowed by the fact that each particle has dimensions which are beyond itself . This would create more space to allow this process to accelerate and thius the universe would grow . At the start though , this would have phenominel energy , and tail off , rather like standard models as new particles came into being .
3. The big bang theory does not say the universe was ever zero size.
See above , this is my weak point and I cant get a theory below 2 equal and opposite fundamental particles in a universe of almost zero size . this gets very close . Maybe tyhe blane theory is correct ?
As a matter of interest: as time is postulated as a particulate property; in fact it doesnt work without it properly , the universe should appear to accelerate when looking at distant stars as time is slower when the light is emitted . The comological redshift shouldnt be constant unless the universe is static . Dark matter : um half the universe is stopping galaxies expanding ...