The speed of magnetization reversal is a key feature in magnetic data storage. Magnetic fields from intense THz pulses have been recently shown to induce small magnetization dynamics in a cobalt thin film on the sub-picosecond time scale. Here, we show that at higher field intensities, the THz electric field starts playing a role, strongly changing the dielectric properties of the cobalt thin film. Both the electronic and magnetic responses are found to occur simultaneously, with the electric field response persistent on a time scale orders of magnitude longer than the THz stimulus.