Next-generation neutrino telescopes with substantially improved sensitivity are required to pinpoint the sources of the diffuse astrophysical neutrino flux detected by IceCube and uncover the century-old puzzle of cosmic-ray origins. A detector near the Equator will provide a unique viewpoint of the neutrino sky, complementing IceCube and other neutrino telescopes in the Northern Hemisphere. Here we present results from an expedition to the northeastern region of the South China Sea, in the western Pacific Ocean. A favourable neutrino telescope site was found on an abyssal plain at a depth of ~3.5 km. At depths below 3 km, the sea current speed, water absorption and scattering lengths for Cherenkov light were measured to be v_c < 10 cm s⁻¹, λ_abs ≈ 27 m and λ_sca ≈ 63 m, respectively. Accounting for these measurements, we present the design and expected performance of a next-generation neutrino telescope, Tropical Deep-sea Neutrino Telescope (TRIDENT). With its advanced photon-detection technology and large dimensions, TRIDENT expects to observe the IceCube steady source candidate NGC 1068 with 5σ significance within 1 year of operation. This level of sensitivity will open a new arena for diagnosing the origin of cosmic rays and probing fundamental physics over astronomical baselines.