The cosmic large-scale structure (LSS) provides a unique testing ground for connecting fundamental physics to astronomical observations. Modeling the LSS requires numerical N-body simulations or perturbative techniques that both come with distinct shortcomings. Here we present the first unified numerical approach, enabled by new time integration and discreteness reduction schemes, and demonstrate its convergence at the field level. In particular, we show that our simulations (i) can be initialized directly at time zero, and (ii) can be made to agree with high-order Lagrangian perturbation theory in the fluid limit. This enables fast, self-consistent, and UV-complete forward modeling of LSS observables.