Emergence of strong-coupling superconductivity and quantum criticality correlated with Lifshitz transitions in the alternate stacking compound 4Hb−TaS2

4Hb-TaS₂ is a naturally formed quasi-two-dimensional heterojunction material composed of alternating monolayers of insulating ($1T$-) and superconducting ($1H$-) TaS₂. We report on a comprehensive high-pressure study on the interplay between charge-density wave (CDW) and superconductivity (SC) in 4Hb-TaS₂. The results uncover a dome-shaped strong-coupling superconductor on the border of a 3 ×{} 3 commensurate CDW at Pc1≈2.0 GPa: (1) nearly one order enhancement of upper critical field Bc2(0); (2) the derived 2Δ₀/kBTc beyond the BCS theory, decaying to a conventional one above 4.5 GPa; (3) the exponent of normal-state resistivity n≈1.50 and triply enhanced electronic effective mass. Under pressure, a third CDW emerging from 2.0 GPa is related to the original two CDWs, then disappears above 11.5 GPa. The temperature dependence of Bc2(T) collapses into a universal curve and the comparison of Bc2(T) to a polar-state function in 4Hb-TaS₂. Theoretical calculations proposed the stronger interlayer coupling and band hybridization responsible for strong-coupling SC; the suppression of new CDWs is related to band inversions between the $1T$-Ta-dxy (GM1+) and S-pz bands (GM2-) at the ΓA point; above 5.0 GPa, the coexisting weak-coupling SC and linear magnetoresistance can be attributed to the formation of electronic bands along the M-K lines and the ΓA point. Our discovery provides an excellent example to demonstrate the interplay of the strong-coupling superconducting state and topological electronic state in van der Waals heterojunctions.