Surveying Galaxy Clusters (in formation) in the Distant Universe

Present-day galaxy clusters are the largest virialized structures in the Universe, yet their early assembly remains poorly understood. At z$>$2, clusters in formation span tens of Mpc and host gas-rich, dust-obscured galaxies embedded in extended, low-surface-brightness gaseous environments. Current (sub-)millimeter facilities lack the mapping speed, sensitivity, and contiguous field of view needed to trace the cold gas and dust driving rapid galaxy growth across such scales. A future large single-dish observatory with degree-scale coverage, broad spectral access, and high-multiplex capability would enable comprehensive and uniform mapping of entire protoclusters, revealing where star formation is triggered or quenched, and quantifying the cold gas budget, thus providing information on gas cooling within protocluster environments. In synergy with wide-sky optical/NIR surveys such as Euclid, LSST, and Roman, this facility would provide the missing multi-scale and multiphase submillimeter view needed to uncover how the stellar, gaseous, and dark-matter components assemble in protoclusters, completing our view of early structure formation.