Lunar mare regolith is traditionally thought to have formed by impact bombardment of newly emplaced coherent solidified basaltic lava. We use new models for initial emplacement of basalt magma to predict and map out thicknesses, surface topographies and internal structures of the fresh lava flows, and pyroclastic deposits that form the lunar mare regolith parent rock, or protolith. The range of basaltic eruption types produce widely varying initial conditions for regolith protolith, including (1) autoregolith, a fragmental meter-thick surface deposit that forms upon eruption and mimics impact-generated regolith in physical properties, (2) lava flows with significant near-surface vesicularity and macroporosity, (3) magmatic foams, and (4) dense, vesicle-poor flows. Each protolith has important implications for the subsequent growth, maturation, and regional variability of regolith deposits, suggesting wide spatial variations in the properties and thickness of regolith of similar age. Regolith may thus provide key insights into mare basalt protolith and its mode of emplacement.