The two-dimensional organic conductor $alpha$-(BEDT-TTF)$_2$I$_3$ undergoes a metal-insulator transition at $T_{rm CO}=135$ K due to electronic charge ordering. We have conducted time-resolved investigations of its electronic properties in order to explore the field- and temperature-dependent dynamics. At a certain threshold field, the system switches from low-conducting to a high-conducting state, accompanied by a negative differential resistance. Our time-dependent infrared investigations indicate that close to $T_{rm CO}$ the strong electric field pushes the crystal into a metallic state with optical properties similar to the one for $T>T_{rm CO}$. Well into the insulating state, however, at $T=80$ K, the spectral response evidences a completely different electronically-induced high-conducting state. Applying a two-state model of hot electrons explains the observations by excitation of charge carriers with a high mobility. They resemble the Dirac-like charge-carriers with a linear dispersion of the electronic bands found in $alpha$-(BEDT-TTF)$_2$I$_3$ at high-pressure. Extensive numerical simulations quantitatively reproduce our experimental findings in all details.