We conducted the simulations in the NVT ensemble, using a system of monoatomic particles (N = 8788) uniformly distributed in cubic boxes of varying side lengths to achieve different densities, across a range of temperatures. This approach allows us to observe phase formation from farfrom-equilibrium states, focusing particularly on liquid-gas coexistence. Although a more precise phase boundary determination could be achieved using more refined techniques such as Histogram Reweighting Monte Carlo, Transition Matrix Monte Carlo, and Expanded Wang-Landau simulations, our primary goal was to compare coexistence phases derived from two-Gaussian filter HhPF simulations with those obtained from MGCM methods.