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ABSTRACT Motivated by the early excess of bright galaxies seen by JWST, we run zoom-in cosmological simulations of a massive galaxy at Cosmic Dawn, in a halo of $$10^{11} {\rm M}_\odot$$ at $z = 9$, using the hydro-gravitational code ramses at an effective resolution $$\sim 10~{\rm pc}$$. We investigate physical mechanisms that enhance the star formation efficiencies (SFEs) at the high gas densities of the star-forming regions in this galaxy ($$\sim 3\times 10^3~{\rm cm^{-3}}$$, $$\sim 10^4~{\rm M}_\odot \,{\rm pc^{-2}}$$). Our fiducial star formation recipe uses a physically motivated, turbulence-based, multi-freefall model, avoiding ad hoc extrapolation from lower redshifts. By $z = 9$, our simulated galaxy is a clumpy, thick, rotating disc with a high stellar mass $$\sim 3\times 10^9~{\rm M}_\odot$$ and high star formation rate $$\sim 50~{\rm M}_\odot \,{\rm yr^{-1}}$$. The high gas density makes supernova (SN) feedback less efficient, producing a high local SFE $$\gtrsim 10~{{\ \rm per\ cent}}$$. The global SFE is set by feedback-driven outflows and only weakly correlated with the local SFE. Photoionization heating makes SN feedback more efficient, but the integrated SFE always remains high. Intense accretion at Cosmic Dawn seeds turbulence that reduces local SFE, but this only weakly affects the global SFE. The star formation histories of our simulated galaxies are similar to observed massive galaxies at Cosmic Dawn, despite our limited resolution. We set the stage for future simulations which treat radiation self-consistently and use a higher effective resolution $$\sim 1~{\rm pc}$$ that captures the physics of star-forming clouds.