Classical fractional crystallization scenarios of early lunar evolution suggest crustal formation by the flotation of light anorthite minerals from a liquid magma ocean. However, this model is challenged by the > 200 Myr age range of primitive ferroan anorthosites, their concordance with Mg-suite magmatism and by the compositional diversity observed in lunar anorthosites. Here, we propose a new model of slushy magma ocean crystallization in which crystals remain suspended in the lunar interior and crust formation only begins once a critical crystal content is reached. Thereafter crustal formation occurs by buoyant melt extraction and magmatism. The mixture viscosity strongly depends on temperature and solid fraction driving the development of a surface stagnant lid where enhanced solidification and buoyant ascent of melt lead to an anorthite-enriched crust. This model explains lunar anorthosites heterogeneity and suggests a crustal formation timescale of 100s Ma, reconciling anorthosite ages with an early age of the Moon.