曙 = 日 (sun) + 署 (signpost / arranged in order). Picture the sun stepping into its appointed place at the horizon — daybreak.
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曙 is bound — you almost never see it alone in modern Chinese. It lives in compounds: 曙光 (shǔguāng, 'first light / hope'), 曙色 (shǔsè, 'dawn light'), 拂曙 (fúshǔ, 'just before dawn').
