We show that the ab initio calculations of nuclear thermodynamics can be performed efficiently using lattice effective field theory. The simulations use a new approach called the pinhole trace algorithm to calculate thermodynamic observables for a fixed number of protons and neutrons enclosed in a finite box. In this framework, we calculate the equation of state, the liquid-vapor coexistence line and the critical point of neutral symmetric nuclear matter with high precision. Since the algorithm uses a canonical ensemble with a fixed number of particles, it provides a sizable computational advantage over grand canonical ensemble simulations that can be a factor of several thousands to as much as several millions for large volume simulations.