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Assembling and maintaining large arrays of individually addressable atoms is a key requirement for continued scaling of neutral-atom-based quantum computers and simulators. In this work, we demonstrate a new paradigm for assembly of atomic arrays, based on a synergistic combination of optical tweezers and cavity-enhanced optical lattices, and the incremental filling of a target array from a repetitively filled reservoir. In this protocol, the tweezers provide microscopic rearrangement of atoms, while the cavity-enhanced lattices enable the creation of large numbers of optical traps with sufficient depth for rapid low-loss imaging of atoms. We apply this protocol to demonstrate near-deterministic filling (99% per-site occupancy) of 1225-site arrays of optical traps. Because the reservoir is repeatedly filled with fresh atoms, the array can be maintained in a filled state indefinitely. We anticipate that this protocol will be compatible with mid-circuit reloading of atoms into a quantum processor, which will be a key capability for running large-scale error-corrected quantum computations whose durations exceed the lifetime of a single atom in the system.