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First recognized by Laplace over two centuries ago, the Moon’s present tidal-rotational bulges are significantly larger than hydrostatic predictions. They are likely relics of a former hydrostatic state when the Moon was closer to the Earth and had larger bulges, and they were established when stresses in a thickening lunar lithosphere could maintain the bulges against hydrostatic adjustment. We formulate the first dynamically self-consistent model of this process and show that bulge formation is controlled by the relative timing of lithosphere thickening and lunar orbit recession. Viable solutions indicate that lunar bulge formation was a geologically slow process lasting several hundred million years, that the process was complete about 4 Ga when the Moon-Earth distance was less than ~32 Earth radii, and that the Earth in Hadean was significantly less dissipative to lunar tides than during the last 4 Gyr, possibly implying a frozen hydrosphere due to the fainter young Sun.