Advances in cosmology and astronomical observations have brought to light significant tensions and uncertainties within the current model of cosmology, which assumes a spatially flat Universe and is known as the ΛCDM model. Moreover, the Planck Legacy 2018 release has preferred that the early Universe had a positive curvature with a confidence level more than 99%. This study reports a quantum mechanism that could potentially replace the concept of dark matter/energy by taking into the account the primordial curvature while generating the present-day spatial flatness. The approach incorporates the primordial curvature as the background curvature to extend the field equations into brane-world gravity. It utilizes a new wavefunction of the Universe that propagates in the bulk with respect to the scale factor and curvature radius of the early Universe upon the emission of the cosmic microwave background. The resulting wavefunction yields both positive and negative solutions, revealing the presence of a pair of entangled wavefunctions as a manifestation of the creation of matter and antimatter sides of the Universe. The wavefunction shows a nascent hyperbolic expansion away from early energy in opposite directions followed by a first decelerating expansion phase during the first ~10 Gyr and a subsequent accelerating expansion phase in reverse directions. During the second phase, both Universe sides are free-falling towards each other under gravitational acceleration. The simulation of the predicted background curvature evolution shows that the early curved background caused galaxies to experience external fields, resulting in the fast orbital speed of outer stars. Finally, the wavefunction predicts that the Universe will eventually undergo a rapid contraction phase resulting in a Big Crunch, which reveals a cyclic Universe.