The natural scenario where dark matter (DM) originates from thermal contact with familiar Standard Model matter in the early universe requires the DM mass to lie within $\sim$MeV to $\sim$10 TeV. Considerable experimental attention has been given to exploring Weakly Interacting Massive Particles (WIMPs) in the upper end of this range, while the sub-GeV region is largely unexplored, even though a thermal origin for dark matter works in a predictive manner in this mass range as well. It is therefore an exploration priority. If there is such an interaction between light DM and ordinary matter, then there necessarily is a production mechanism in accelerator-based experiments. The Light Dark Matter eXperiment (LDMX) is a planned electron-beam fixed-target missing-momentum experiment with unique sensitivity to sub-GeV light DM. These proceedings will discuss the background rejection capabilities and the projected sensitivities of the experiment after an accelerator upgrade from 4 to 8 GeV beam energy, where most of LDMX's data will be collected.