Soft leptogenesis is a mechanism which generates the matter-antimatter asymmetry of the Universe via the out-of-equilibrium decays of heavy sneutrinos in which soft supersymmetry breaking terms play two important roles: they provide the required $CP$ violation and give rise to the mass splitting between otherwise degenerate sneutrino mass eigenstates within a single generation. This mechanism is interesting because it can be successful at the lower temperature regime $T\ensuremath{\lesssim}1{0}^{9}\text{ }\text{ }\mathrm{GeV}$ in which the conflict with the overproduction of gravitinos can possibly be avoided. In earlier works, the leading $CP$ violation is found to be nonzero only if finite temperature effects are included. By considering generic soft trilinear couplings, we find two interesting consequences: (1) the leading $CP$ violation can be nonzero even at zero temperature realizing nonthermal $CP$ violation, and (2) the $CP$ violation is sufficient even far away from the resonant regime allowing soft supersymmetry breaking parameters to assume natural values at around the TeV scale. We discuss phenomenological constraints on such scenarios and conclude that the contributions to charged lepton flavor violating processes are close to the sensitivities of present and future experiments.