Nucleosynthetic isotope variability among Solar System objects is often used to probe the genetic relationship between meteorite groups and the rocky planets (Mercury, Venus, Earth and Mars), which, in turn, may provide insights into the building blocks of the Earth-Moon system. Using this approach, it has been inferred that no primitive meteorite matches the terrestrial composition and the protoplanetary disk material from which Earth and the Moon accreted is therefore largely unconstrained. This conclusion, however, is based on the assumption that the observed nucleosynthetic variability of inner-Solar-System objects predominantly reflects spatial heterogeneity. Here we use the isotopic composition of the refractory element calcium to show that the nucleosynthetic variability in the inner Solar System primarily reflects a rapid change in the mass-independent calcium isotope composition of protoplanetary disk solids associated with early mass accretion to the proto-Sun. We measure the mass-independent 48 Ca/ 44 Ca ratios of samples originating from the parent bodies of ureilite and angrite meteorites, as well as from Vesta, Mars and Earth, and find that they are positively correlated with the masses of their parent asteroids and planets, which are a proxy of their accretion timescales. This correlation implies a secular evolution of the bulk calcium isotope composition of the protoplanetary disk in the terrestrial planet-forming region. Individual chondrules from ordinary chondrites formed within one million years of the collapse of the proto-Sun reveal the full range of inner-Solar-System mass-independent 48 Ca/ 44 Ca ratios, indicating a rapid change in the composition of the material of the protoplanetary disk. We infer that this secular evolution reflects admixing of pristine outer-Solar-System material into the thermally processed inner protoplanetary disk associated with the accretion of mass to the proto-Sun. The identical calcium isotope composition of Earth and the Moon reported here is a prediction of our model if the Moon-forming impact involved protoplanets or precursors that completed their accretion near the end of the protoplanetary disk's lifetime.