A Kinetic Monte Carlo scheme is applied to simulate with atomic resolution the synthesis of mono (few) layer (s) graphene (Gr) from a silicon carbide (SiC) substrate by selective evaporation of silicon (Si) atoms. The simulation computes the individual dynamics of the residual carbon (C) atoms which diffuse and reconfigure starting from the positions occupied in the SiC hexagonal lattice to the final Gr honeycomb structure. During the transition they gradually modify hybridization (from sp 3 to sp 2) and bond partners (from Si-C to CC). We demonstrate that our method is able to recover the complex evolution steps of the epitaxial Gr on SiC in large systems for large time intervals. Moreover, the simulation results can be validated directly by means of comparison with experimental data when varying the material (eg initial surface configuration or polarity) or process (eg temperature and pressure) conditions.