We derive conservative upper limits on the dark-matter–nucleon scattering cross-section for sub-GeV mass dark matter. Working exclusively within the low-energy chiral effective theory, we derive bounds that are independent of the details of the dark matter interactions in the UV. Dark matter that interacts only hadronically at leading order also inevitably interacts with photons or electrons at next-to-leading-order. We show that these electromagnetic interactions lead to strong constraints from big bang nucleosynthesis and over-production of dark matter via freeze-in at low temperatures, while the leading-order hadronic couplings face stringent constraints from meson decays. Combining these constraints, we rule out both spin-independent and spin-dependent dark-matter–nucleon scattering cross-sections $\gtrsim 10^{-36}\,{\rm cm}^2$ for dark matter masses in the keV - 100 MeV range. These bounds are several orders of magnitude stronger than the existing constraints from astrophysics and cosmology and have significant implications for future low-mass direct detection experiments.