Pushing nanoscale optical confinement to its ultimate limits defines the regime of nano-cavity quantum electrodynamics (nano-cQED), where light--matter interactions approach the fundamental quantum limits of individual atoms, e.g., picocavities. However, realizing such extreme confinement in a stable and controllable manner remains a key challenge. Here, we introduce a van der Waals material-based nano-cQED platform by coupling monolayer MoS2 excitons to plasmonic sub-nanocavities formed via assembly of ultrasmall gold clusters (3-5 nm) in the nanogap of a nanoparticle-on-mirror nanocavity. These clusters emulate the field-confining role of atomic protrusions of the picocavities through a resonance-insensitive lightning-rod effect, achieving deep-subwavelength mode volumes. In this nano-cQED testbed, we observe pronounced multi-branch Rabi splittings and ultrastrong lower-branch polaritonic photoluminescence with up to 10^4-fold enhancement. This deterministic architecture provides a controllable pathway to access picocavity-like behavior and opens new opportunities for single-molecule spectroscopy and the exploration of nano-cQED.