We experimentally demonstrate the decomposition of heat dissipation during free-energy generation in a nanometer-scale dot transitioning to a non-equilibrium steady state via single-electron counting statistics. An alternating-current signal driving a reservoir that injects multiple electrons into the dot makes it non-equilibrium, leading to free-energy generation, heat dissipation, and Shannon-entropy production. By analyzing the time-domain probability distributions of multi-electron states of the dot, we quantitatively decompose the heat dissipation into housekeeping and excess heats, thereby revealing their direct correlation with free-energy generation. This correlation suggests that the ratio of the generated free energy to the work applied to the dot, can potentially reach 0.5 under far-from-equilibrium conditions induced by a large signal, while an efficiency of 0.25 was experimentally achieved. These results establish a quantitative link between decomposed heat dissipation and free-energy generation in a multi-electron stochastic system, providing a thermodynamic framework for non-equilibrium electronic devices.