The Galactic Center hosts the densest known stellar environment in the Milky Way, dominated by the massive black hole Sgr A* and the surrounding nuclear star cluster. Theory predicts that this region should also contain a large population of stellar compact objects (SCOs)---black holes, neutron stars, and white dwarfs---forming a ``dark cluster'' whose distribution and properties remain observationally unconstrained. These unseen stellar remnants are central to questions of mass segregation, cluster dynamics, and the expected rate of extreme mass ratio inspirals (EMRIs) detectable by future gravitational-wave observatories including LISA. Current evidence for SCOs in the Galactic Center is indirect, relying on dynamical mass measurements, X-ray surveys, and a small number of transient sources. Direct detections remain elusive due to crowding, extinction, and the sensitivity limits of existing instruments. We explore how upcoming facilities, in particular the Extremely Large Telescope (ELT) with its first-light imager MICADO, can fundamentally transform this field. MICADO’s combination of deep photometry, high spatial resolution, and precise astrometry will enable systematic searches for SCO-star binaries via photometric variability and orbital astrometric signatures, as well as direct detection of isolated accreting black holes interacting with the gas-rich Galactic Center environment. We outline the observational pathways, technical challenges, and expected sensitivities, showing that ELT/MICADO observations can provide the first quantitative constraints on the dark cluster population. Establishing these constraints will be pivotal for understanding the dynamical evolution of the Galactic Center, the role of compact remnants in nuclear star clusters, and the astrophysical context of gravitational-wave sources in galactic nuclei.
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