The presence of isotope heterogeneity of nucleosynthetic origin amongst meteorites and their components provides a record of the diverse stars that contributed matter to the protosolar molecular cloud core. Understanding how and when the solar system's nucleosynthetic heterogeneity was established and preserved within the solar protoplanetary disk is critical for unraveling the earliest formative stages of the solar system. Here, we report calcium and magnesium isotope measurements of primitive and differentiated meteorites as well as various types of refractory inclusions, including refractory inclusions (CAIs) formed with the canonical ²⁶Al/²⁷Al of ~5×10^-5 (²⁶Al decays to ²⁶Mg with a half-life of ~0.73Ma) and CAIs that show fractionated and unidentified nuclear effects (FUN-CAIs) to understand the origin of the solar system's nucleosynthetic heterogeneity. Bulk analyses of primitive and differentiated meteorites along with canonical and FUN-CAIs define correlated, mass-independent variations in ⁴³Ca, ⁴⁶Ca and ⁴⁸Ca. Moreover, sequential dissolution experiments of the Ivuna carbonaceous chondrite aimed at identifying the nature and number of presolar carriers of isotope anomalies within primitive meteorites have detected the presence of multiple carriers of the short-lived ²⁶Al nuclide as well as carriers of anomalous and uncorrelated ⁴³Ca, ⁴⁶Ca and ⁴⁸Ca compositions, which requires input from multiple and recent supernovae sources. We infer that the solar system's correlated nucleosynthetic variability reflects unmixing of old, galactically-inherited homogeneous dust from a new, supernovae-derived dust component formed shortly prior to or during the evolution of the giant molecular cloud parental to the protosolar molecular cloud core. This implies that similarly to ⁴³Ca, ⁴⁶Ca and ⁴⁸Ca, the short-lived ²⁶Al nuclide was heterogeneously distributed in the inner solar system at the time of CAI formation.