Is dark matter a thermal-relic weakly interacting massive particle?

Does a particle of mass $1\,\mathrm{GeV}\text{ to }100\,\mathrm{TeV}$, produced by thermal freeze-out with annihilation cross section $\langle \sigma v\rangle \sim 3 \times 10^{-26}\,\mathrm{cm}^{3}/\mathrm{s}$, make up $\Omega_c$? Answer yes (a detection of nuclear recoils, annihilation products or collider production consistent with the thermal cross section) or no for named benchmarks: exclusion of Higgs-portal and Z-portal thermal relics by direct detection, and of the pure wino ($\sim 2.9\,\mathrm{TeV}$) and pure Higgsino ($\sim 1.1\,\mathrm{TeV}$) thermal relics by gamma-ray line and continuum searches from the Galactic Center. Thermal relics with loop-suppressed nuclear couplings (pure Higgsino, $\sigma_{\mathrm{SI}} \sim 10^{-49}\text{ to }10^{-48}\,\mathrm{cm}^{2}$) lie at or below the xenon neutrino background floor, so direct detection alone cannot close the question.

Liquid-xenon or argon detectors reaching the neutrino background floor over $10\,\mathrm{GeV}$ to $10\,\mathrm{TeV}$, combined with gamma-ray line and continuum searches sensitive to wino and Higgsino annihilation at the thermal cross section.