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The volume and composition of Earth's earliest continental crust is a matter of ongoing debate, but is an essential component of solid-Earth evolution, relating to mantle dynamics and the origin of plate tectonics. The isotopic composition of titanium within sedimentary rocks, a suggested proxy for protolith composition, suggests the early emergence of an evolved continental crust. Other geochemical proxies such as Ni/Co and Cr/Zn ratios suggest a more mafic early crust. Important to understanding the differences between these proxy-based interpretations of crustal growth and composition is the mechanism of crustal chemical evolution. Two key processes may occur: weathering, whereby cations are selectively removed from the continents and transported to the oceans; and igneous differentiation. Resolving these processes is hampered by the ability to deconvolve their compositional effects. To overcome this, we derive a predictive and invertible model of sedimentary major-element composition that reconstructs protolith composition, and hence that of the crust, whilst accounting for the effect of weathering. We compile a dataset of sedimentary rock, river sediment, soil, and igneous rock compositions. By applying principal component analysis to the log-ratio transformed compositional dataset we show that any composition can be well described by considering just two linear vectors of igneous evolution and weathering. We thus define a model for sedimentary composition as a linear combination of these two processes, which allows us to undo the compositional effect of weathering to reconstruct the major element composition of protoliths and thereby average upper continental crust through time. We find that the major-element composition of the modern upper continental crust has been modified by weathering relative to pristine igneous rocks. We calculate the amount of each element that must be lost to sufficiently modify the crustal composition. By extrapolating modern weathering rates over the age of the crust we conclude that a significant amount of weathering restite has likely been subducted into the mantle indicating a crust-to-mantle recycling rate of 1.47 ± 1.00 ×1013kg yr-1. Secondly we apply our model to the extensive dataset of sedimentary rocks compiled by the Sedimentary Geochemistry and Paleoenvironments Project from across the stratigraphic record so as to reconstruct the composition of the ancient crust. We find that the Archean upper continental crust is more mafic than present day, but stabilised into the present evolved composition by 2.5 - 2.0 Ga.