In recent years, the threshold of Dark Matter search experiments has been lowered, enabling the search for Dark Matter-electron scattering. In the region of interest for mass and cross-section that current experiments can reach, the propagation of particles from the Dark Matter wind through the Earth can produce a (sideral) daily modulation in the observed signal. We explore the modulation signal expected in different materials and show how a significant improvement in the current sensitivity can be obtained in the lower mass region by searching for that daily modulation. Depending on the mediator, mass, and cross-section of interest, we study the dependence of the sensitivity on the latitude of the experiment.