The initial conditions of our Universe are a fundamental property of our Universe. Together with the laws of physics, they determine its phenomenological appearance and dynamical evolution. However, the physical processes determining the origin of cosmic structure and the accelerating cosmic expansion remain mysterious. Cosmology now turns to search for observational fingerprints robustly predicted by physical models within the spatial distribution of cosmic matter as traced by galaxies in cosmological surveys. According to the current paradigm, all observable structures originate from primordial quantum fluctuations generated during the early epoch of inflation in a hot "Big Bang". These seed fluctuations grew via gravitational amplification to form a giant cosmic web of dark matter, eventually aggregating into massive clusters and filamentary cosmic structures. The detailed spatial configuration and dynamics of the cosmic matter distribution retain a memory of the initial conditions, and additionally encode the physical processes that shaped it over 13.8 billion years of cosmic history. Detailed reconstructions of the spatial matter distribution and its dynamics from galaxy surveys provides us with important information to test fundamental physics, and study the evolution of the Universe. Over a five-year campaign, we seek to reconstruct the cosmic initial conditions over a significant fraction of the observable Universe, aiming to construct a physically consistent computer model of our Universe using novel data science techniques and next-generation cosmological observations. We will use novel data analysis and machine learning techniques developed by our group to reconstruct, for the first time, the largest and most detailed map of the three-dimensional seed fluctuations from which observed structures formed. Specifically, we will use extensions of our algorithm, "Bayesian Origin Reconstruction from Galaxies" (BORG), to fit cosmological N-body simulations in their full generality to the available galaxy catalogs of the SDSS-III's Baryon Oscillation Spectroscopic Survey (BOSS). Additional surveys, such as the Euclid satellite mission, SphereX, and the Vera Rubin Observatory, will soon commence operations, providing unprecedented amounts of data. Using such data, we seek to infer the cosmic matter distribution over an unprecedented cosmological volume of (4 Gpc)^3. The obtained results will be used to study the true nature of our cosmic origin, and test the theory of inflation. We will also constrain cosmological parameters, specifically the equation of state of dark energy, which is held responsible for the currently observed accelerating expansion of the Universe. We also aim at cross-analyzing our reconstructed dark matter maps with observations of the cosmic microwave background (CMB). The project is especially timely with respect to upcoming cosmological surveys. Besides producing significant scientific results, the proposed project also acts as a necessary precursor for the next generation of galaxy surveys, e.g., the Vera Rubin Observatory’s Legacy Survey of Space and Time, or the Euclid satellite. We will further provide the community with accurate and detailed reconstructions of the cosmic matter distribution and velocity fields, facilitating many complimentary research projects with collaborators, multiplying the scientific outcome of the proposed research.