  Off-equilibrium dynamics of a three-dimensional lattice model with nearest-
and next nearest-neighbors exclusions is studied. At equilibrium, the model
undergoes a first-order fluid-solid transition. Non-equilibrium filling,
through random sequential adsorption with diffusion, creates amorphous
structures and terminates at a disordered state with random closest packing
density that lies in the equilibrium solid regime. The approach towards random
closest packing is characterized by two distinct power-law regimes, reflecting
the formation of small densely packed grains in the long time regime of the
filling process. We then study the fixed-density relaxation of these amorphous
structures towards the solid phase. The route to crystallization is shown to
deviate from the simple grain growth proposed by classical nucleation theory.
Our measurements suggest that relaxation is driven mainly by coalescence of
neighboring crystallized grains which exist in the initial amorphous state.
