We will realize a new scenario of the Big Bang as a transition between a pregeometric phase with no notion of spacetime, to a phase in which the Universe is described by a smooth spacetime, within a complete Quantum Gravity framework. The framework is that of group field theories (GFTs), building on a recent flourishing of results and also on insights from loop quantum gravity, matrix models and simplicial gravity. The Big Bang is a condensation of fundamental GFT quanta into a macroscopic spacetime fluid, with general relativity as its hydrodynamics. We will connect for the first time in a rigorous way quantum gravity models to effective models in cosmology and explore the consequences of this scenario on the physics of anisotropies and inhomogeneities. The research program is inherently interdisciplinary, with condensed matter methods (theory of quantum fluids) combined with quantum gravity models, to solve fundamental problems in physical cosmology. It will be carried out in the ideal environment of the Albert Einstein Institute, hosting top quality research groups in quantum gravity and cosmology, and it will involve hiring two postdocs for a total of 33 months. It will open up a tantalizing new conceptual and mathematical understanding of gravity and the cosmos.