Classical cosmology is grounded in general relativity, a theory of gravitation that breaks down when describing the evolution of the universe at a time before the Planck time. Before the Planck time the quantum effects of the gravitational field become important due to the high energies and small distances involved. The description of the initial singularity is therefore in the realm of quantum cosmology.
There exist some models of quantum cosmology that would correspond somehow to what you imagine or consider an origin of the universe due to a quantum fluctuation. These are models of canonical quantum cosmology, that describes the dynamics of the wavefunction of the universe in a similar way than quantum mechanics describes the dynamics of the wavefunction of a single particle. Based on this results, similar consistency conditions that lead to a theory of multiple particles that can be created and annihilated (quantum field theory), may allow to formulate a model of multiple (baby) universes that may be created and annihilated as quantum fluctuations.
These are imaginative ideas but far too speculative, with too many open problems (for example, all three issues mentioned by ueit would apply to such models), and without any expectation to be experimentally verified in a near future.