The EDELWEISS collaboration has performed a search for dark matter particles with masses below the GeV-scale with a 33.4-g germanium cryogenic detector operated in a surface lab. The energy deposits were measured using a neutron-transmutation-doped Ge thermal sensor with a 17.7~eV (RMS) baseline heat energy resolution leading to a 60~eV analysis energy threshold. Despite a moderate lead shielding and the high-background environment, the first sub-GeV spin-independent dark matter limit based on a germanium target has been achieved. The experiment provides the most stringent, nuclear recoil based, above-ground limit on spin-independent interactions above 600~MeV/c$^{2}$. The experiment also provides the most stringent limits on spin-dependent interactions with protons and neutrons below 1.3~GeV/c$^{2}$. Furthermore, the dark matter search results were studied in the context of Strongly Interacting Massive Particles, taking into account Earth-shielding effects, for which new regions of the available parameter space have been excluded. Finally, the dark matter search has also been extended to interactions via the Migdal effect, resulting for the first time in the exclusion of particles with masses between 45 and 150~MeV/c$^{2}$ with spin-independent cross sections ranging from $10^{-29}$ to $10^{-26}$~cm$^2$.
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