Abstract <p>We analyze a quantum-mechanical counterpart of Newtonian cosmology and show that the effects of zero-point motion eliminate the classical density singularity. Quantum effects are particularly significant for closed Universes where without the cosmological constant the energy spectrum and space curvature are quantized. When a small positive cosmological constant is included, these states become quasistationary and decay via tunneling. Corresponding metastable Universes evolve in three stages: a long period of gestation followed by rapid tunneling expansion further followed by slower Hubble expansion. This closely resembles an inflation scenario of modern cosmology.</p>