The dynamical and chemical signatures of a planetary system are independent fossil records of its past. Orbital parameters are vestiges of its formation and dynamical evolution, while chemical compositions of planets and hosts are fingerprints of the stellar nursery and the protoplanetary disk where they formed. In this talk, I will explain the cutting-edge techniques I am using to measure orbital parameters and compositions and how to leverage them to reconstruct the history of planetary systems at a population scale. Obtaining these measurements in a volume-limited sample will enable robust statistics to develop a probabilistic model of formation mechanisms, observationally constraining their transition from stellar binary to planetary formation for the first time. This analysis will lead to the identification of spectroscopic signatures of formation with next generation observatories as we take our first steps towards a comprehensive theory of star and planet formation to uncover our cosmic origins.