The quantitative description of correlated electron materials remains a modern computational challenge. We demonstrate a numerical strategy to simulate correlated materials at the fully ab initio level beyond the solution of effective low-energy models and apply it to gain a detailed microscopic understanding across a family of cuprate superconducting materials in their parent undoped states. We uncover microscopic trends in the electron correlations and reveal the link between the material composition and magnetic energy scales through a many-body picture of excitation processes involving the buffer layers. Our work illustrates a path toward a quantitative and reliable understanding of more complex states of correlated materials at the ab initio many-body level.