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ABSTRACT We investigate the formation (spin-up) of galactic discs in the artemis simulations of Milky Way (MW)-mass galaxies. In almost all galaxies, discs spin up at higher [Fe/H] than the MW. Those galaxies that contain an analogue of the Gaia Sausage-Enceladus (GSE) spin up at a lower average metallicity than those without. We identify six galaxies with spin-up metallicity similar to that of the MW, which formed their discs ∼8–11 Gyr ago. Five of these experience a merger similar to the GSE. The spin-up times correlate with the halo masses at early times: galaxies with early spin-up have larger virial masses at a lookback time tL = 12 Gyr. The fraction of stars accreted from outside the host galaxy is smaller in galaxies with earlier spin-ups. Accreted fractions small enough to be comparable to the MW are only found in galaxies with the earliest disc formation and large initial virial masses (M200c ≈ 2 × 1011 M⊙ at tL = 12 Gyr). We find that discs form when the halo’s virial mass reaches a threshold of M200c ≈ (6 ± 3) × 1011 M⊙, independent of the spin-up time. However, the failure to form a disc in other galaxies appears to be instead related to mergers at early times. We also find that discs form when the central potential is not particularly steep. Our results indicate that the MW assembled its mass and formed its disc earlier than the average galaxy of a similar mass.