Schematic of the direct injection of SLRs into the early Solar System within the birth cluster. Massive stars those were born in the cluster would trigger CCSNe when they finished their lifetime, t_⋆. To explain the coexistence of ²⁶Al-rich and ²⁶Al-poor CAIs in the early Solar System, a direct injection of SLR-rich dust grains from a CCSN should occur during CAI formation in the Solar System. A necessary condition for Solar System formation is that at least one CCSN occurs in the birth cluster within the duration of star formation, t_SF.