It remains a fundamental mystery: why is the Universe made of matter rather than antimatter, when equal numbers of matter and antimatter particles were created just after the Big Bang? Astronomical observations show that since then, essentially all the antimatter annihilated with matter, turning back into energy. However, a tiny fraction of excess matter was left over, forming all the objects in the Universe today. While the current model for all known fundamental forces and particles cannot explain how the excess matter survived, recent mathematical theories explain the matter-antimatter asymmetry by positing new, as-yet undiscovered, forces and particles. In most of these theories, the new fundamental phenomena also cause a tiny yet detectable deformation in the distribution of electric charge in ordinary atomic nuclei, known as a Schiff moment (SM). Our goal is to discover evidence for such new particles and forces by measuring a nuclear SM. We will construct a novel apparatus that uses a cryogenic beam of diatomic molecules to detect a nuclear SM. We provide detailed estimates indicating that our approach will provide a 100-fold increase in sensitivity, relative to the current state of the art, to certain forces that could be responsible for the matter-antimatter asymmetry. This project seeks to answer the question: how was matter slightly preferred over antimatter just after the Big Bang, resulting in the physical Universe seen today?