We elaborate on the compatibility of a Presentism perspective with Special Relativity. Specifically, we first introduce a description of evolution in present instants and connect it with the recent studies on the discreteness of time and space. Then, to interpret time dilations and length contractions in Presentism, we consider the perspective of a free massive particle. In the context of a finite information density, we describe how a discrete, relational, and relativistic spacetime emerges from the sampling of information in a 3D imaginary space lattice evolving in atomic present instants.