ABSTRACT We explore the build-up of quiescent galaxies using a sample of 28 469 massive (M⋆ ≥ 1011 M⊙) galaxies at redshifts 1.5 < $z$ < 3.0, drawn from a 17.5 deg2 area (0.33 Gpc3 comoving volume at these redshifts). This allows for a robust study of the quiescent fraction as a function of mass at 1.5 < $z$ < 3.0 with a sample ∼40 times larger at log(M⋆/$\rm M_{⊙ })\ge 11.5$ than previous studies. We derive the quiescent fraction using three methods: specific star formation rate, distance from the main sequence, and UVJ colour–colour selection. All three methods give similar values at 1.5 < $z$ < 2.0, however the results differ by up to a factor of 2 at 2.0 < $z$ < 3.0. At redshifts 1.5 < $z$ < 3.0, the quiescent fraction increases as a function of stellar mass. By $z$ = 2, only 3.3 Gyr after the big bang, the universe has quenched ∼25 per cent of M⋆ = 1011 M⊙ galaxies and ∼45 per cent of M⋆ = 1012 M⊙ galaxies. We discuss physical mechanisms across a range of epochs and environments that could explain our results. We compare our results with predictions from hydrodynamical simulations SIMBA and IllustrisTNG and semi-analytic models (SAMs) SAG, SAGE, and Galacticus. The quiescent fraction from IllustrisTNG is higher than our empirical result by a factor of 2–5, while those from SIMBA and the three SAMs are lower by a factor of 1.5–10 at 1.5 < $z$ < 3.0.