Based on the recent experiments on the triangular lattice antiferromagnet Na2BaCo(PO4)2, we propose the easy-axis XXZ spin-1/2 model on the triangular lattice, that exhibits a quantum spin supersolid, to be a precursory Dirac spin liquid. Despite the presence of a three-sublattice magnetic order as a spin supersolid, we suggest that this system is close to a Dirac spin liquid by exploring its spectroscopic response. The physical consequence is examined from the spectroscopic response, and we establish the continuous spectra near the M point in addition to the K point excitation from the spinon continuum on top of the three-sublattice order. Moreover, the satellite peaks were predicted at the mid-points connecting the Γ and K points. This proposal offers a plausible understanding of the recent inelastic neutron scattering measurement in Na2BaCo(PO4)2 and could inspire further research in relevant models and materials, such as K2Co(SeO3)2 and Rb2Co(SeO3)2, and even more anisotropic magnets like PrMgAl11O19. Published by the American Physical Society 2024

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