This study investigates how molecular softening influences the thermomechanical and topological properties of crosslinked epoxy networks through molecular dynamics simulations. A logarithmically distributed softening factor was introduced prior to curing, spanning values of 0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 1, 2, 5, and 10. This factor was used to systematically modify selected force-field parameters, namely OPLS-type dihedral coefficients and harmonic angle coefficients, in order to tune the intrinsic rigidity of the molecular building blocks. For each factor, two system sizes were generated: a small system (S) containing 192 molecules and a medium system (M) containing 2187 molecules, both with a stoichiometric ratio of 2 DGEBA:1 DAAE. For each size and factor, ten independent initial configurations were prepared, each corresponding to a distinct atomic arrangement prior to crosslinking. After applying the softening factor, curing was performed in LAMMPS using the fix bond/create approach, and the crosslinking kinetics were monitored throughout the process. The resulting networks were then analyzed in terms of both thermomechanical response and topology using in-house topological analysis algorithms. The results demonstrate that controlling molecular rigidity provides a powerful lever to significantly alter, and potentially tailor, both the topological organization and thermomechanical behavior of the cured networks. These findings highlight molecular softening as an effective strategy for steering the structure–property relationships of thermoset polymer systems.