Despite mounting evidence that dark matter (DM) exists in the Universe, its fundamental nature remains unknown. We present sensitivity estimates to detect DM particles with a future very-high-energy ($gtrsim$ TeV) wide field-of-view gamma-ray observatory in the Southern Hemisphere. This observatory would search for gamma rays from the annihilation or decay of DM particles in the Galactic halo. With a wide field of view, both the Galactic Center and a large fraction of the Galactic halo will be detectable with unprecedented sensitivity to DM in the mass range of $sim$500 GeV to $sim$2 PeV. These results, combined with those from other present and future gamma-ray observatories, will likely probe the thermal relic annihilation cross section of Weakly Interacting Massive Particles for all masses from $sim$80 TeV down to the GeV range in most annihilation channels.
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