Refractory inclusions [Ca-Al-rich Inclusions (CAIs) and Amoeboid Olivine Aggregates (AOAs)] in primitive meteorites are the oldest Solar System solids. They formed in the hot inner protoplanetary disk and, as such, provide insights into the earliest disk dynamics and physicochemical processing of the dust and gas that accreted to form the Sun and its planetary system. Using the short-lived ²⁶Al to ²⁶Mg decay system, we show that bulk refractory inclusions in CV (Vigarano-type) and CR (Renazzo-type) carbonaceous chondrites captured at least two distinct ²⁶Al-rich (²⁶Al/²⁷Al ratios of ∼5 × 10⁻⁵) populations of refractory inclusions characterized by different initial ²⁶Mg/²⁴Mg isotope compositions (μ²⁶Mg*₀). Another ²⁶Al-poor CAI records an even larger μ²⁶Mg*₀ deficit. This suggests that formation of refractory inclusions was punctuated and recurrent, possibly associated with episodic outbursts from the accreting proto-Sun lasting as short as <8000 yr. Our results support a model in which refractory inclusions formed close to the hot proto-Sun and were subsequently redistributed to the outer disk, beyond the orbit of Jupiter, plausibly via stellar outflows with progressively decreasing transport efficiency. We show that the magnesium isotope signatures in refractory inclusions mirrors the presolar grain record, demonstrating a mutual exclusivity between ²⁶Al enrichments and large nucleosynthetic Mg isotope effects. This suggests that refractory inclusions formed by incomplete thermal processing of presolar dust, thereby inheriting a diluted signature of their isotope systematics. As such, they record snapshots in the progressive sublimation of isotopically anomalous presolar carriers through selective thermal processing of young dust components from the proto-Solar molecular cloud. We infer that ²⁶Al-rich refractory inclusions incorporated ²⁶Al-rich dust which formed <5 Myr prior to our Sun, whereas ²⁶Al-poor inclusions (such as FUN- and PLAC-type CAIs) incorporated >10 Myr old dust.