It's not just assumed, it is predicted by the fact that at high enough energies, the fundamental forces begin to break down and unify in symmetry. The electromagnetic force and weak interaction unify at relatively low energy and so it's been verified. The strong interaction takes considerably more energy to unify with the electroweak force, however, through work in the field of quantum chromodynamics, it is all but certain that these fundamental force of quantum mechanics can be unified at high enough energy. To obtain this sort of energy, providing there is no external source to fuel our universe, the only conclusion is that the universe was considerably smaller--and a size can be calculated. It's also been predicted that the gravitational force can be unified into a supersymmetry with quantum mechanics, giving rise to terms like 'the theory of everything.' Whether you believe general relativity to be unifiable with QM or that GR is more fundamental than QM, one thing is certain, the size of the universe in order to unify the strong, weak, and electromagnetic forces is knowable and we've done our best to estimate it based on our conclusions of the energies they will unify at.
So, it goes beyond the realm of an 'assumption,' although, true it is still highly uncertain a singularity is in fact the initial state of a universe to-be.
However, if indeed a universe were to suddenly pop into existence and underwent cosmic inflation--we'd never see it. The expansion would be faster than light and the bubble would in some way consume us all-- assuming we were inside the radius of the inflation caused expansion.
The best answer I can give as to why no universes will spontaneously appear within our universe is linked to the cosmic censorship hypothesis, whereby, if indeed the universe began as a singularity, it is of a unique character--unifying all fundamental forces into a supersymmetry, then, no singularity that is to manifest within the universe created from this initial state can reattain this state of supersymmetry and thereby, no universes can arise within another. To do so would destroy the parent universe--plus the singularity would have to literally pull the entire universe into itself which is not terribly likely--especially since there are a large number of these entities populating the universe and we are still here. The possibility is still there though, I would assume, but unlikely.
As for matter or matter-like material, it does come into existence always, popping in and out of existence [virtual particles]. They 'borrow' the energy to manifest, cause some effect, and blip back out of existence. What prevents matter from being created and existing on a more long term scale is due to energetics and some quantum mechanics. You have to have free quarks, or other fundamental particles in order to be able to create new interactions between them that lead to particles like a proton and neutron. To free up quarks takes a considerable amount of energy... and to make new quarks requires even more energy--energy levels you won't often find in the universe, if at all--except during the Big Bang.