The primordial Universe offers a unique opportunity to test physics of the microscopic world with observations on cosmic scales. In this project, I have systematically looked into the cosmological correlators from the baby Universe, i.e. spatial correlations of matter distributions in the earliest moment of the Universe. The focus is the observable imprints of fundamental symmetries in these correlators, and the main computational tool is a new approach called the cosmological bootstrap. The research output contains a complete set of detectable predictions from the primordial Universe, and the first observational data analysis for these new signatures.