  We introduce and analyze a space-time hybridized discontinuous Galerkin
method for the evolutionary Navier--Stokes equations. Key features of the
numerical scheme include point-wise mass conservation, energy stability, and
pressure robustness. We prove that there exists a solution to the resulting
nonlinear algebraic system in two and three spatial dimensions, and that this
solution is unique in two spatial dimensions under a small data assumption. A
priori error estimates are derived for both the velocity and pressure.
