Since we can get energy from the Sun, either directly or indirectly through fossil fuels, and we can use this energy to drive our motors which release energy in the form of heat (back into the atmosphere), kinetic, sound, or electricity.
But we are not really releasing the energy originally acquired from the sun back into the universe.
So is Earth, as a system, gaining energy as time passes?
You said
But we are not really releasing the energy originally acquired from the sun back into the universe.
Why not? Earth has a non-zero temperature and thus it is radiating like a black body releasing energy outside. We can even try to evaluate the Earth temperature by requiring such a balance between receieved and radiated energy. Every black body radiates a power per unit area given by Stefan-Boltzmann law
$$j=\sigma T^4$$
where $\sigma$ is the Stefan-Boltzmann constant. Lets denote by $R_{\rm sun}$ the sun's radius, by $R_{\rm Earth}$ the Earth radius and by $L_{\rm sun}$ the distance between Earth and sun. It is straight forward to see that the power that arrives the Earth surface is
$$P_{\rm in\:Earth}=\pi R_{\rm Earth}^{2}\frac{4\pi R_{\rm sun}^2}{4\pi L_{\rm sun}^2}\sigma T_{\rm sun}^4=\pi R_{\rm Earth}^{2}\frac{R_{\rm sun}^2}{L_{\rm sun}^2}\sigma T_{\rm sun}^4$$
This power should be balanced by the power emitted by Earth
$$P_{\rm out\:Earth}=4\pi R_{\rm Earth}^2\sigma T_{\rm Earth}^4$$
Comparing those expressions we obtain
$$T_{\rm Earth}=\sqrt{\frac{R_{\rm sun}}{2L_{\rm sun}}}T_{\rm sun}\approx 280^\circ{\rm K}\approx 7^\circ{\rm C}$$
which is not too far from the average temperature of Earth which from the internet is around $14^\circ{\rm C}$. This implies that we are not far from equilibrium with the Earth environment.
