ABSTRACT We study the growth of stellar discs of Milky Way-sized galaxies using a suite of cosmological simulations. We calculate the half-mass axis lengths and axis ratios of stellar populations split by age in galaxies with stellar mass $M_{*}=10^7\!-\!10^{10}\, \mathrm{M}_{⊙ }$ at redshifts z > 1.5. We find that in our simulations stars always form in relatively thin discs, and at ages below 100 Myr are contained within half-mass height z1/2 ∼ 0.1 kpc and short-to-long axial ratio z1/2/x1/2 ∼ 0.15. Disc thickness increases with the age of stellar population, reaching median z1/2 ∼ 0.8 kpc and z1/2/x1/2 ∼ 0.6 for stars older than 500 Myr. We trace the same group of stars over the simulation snapshots and show explicitly that their intrinsic shape grows more spheroidal over time. We identify a new mechanism that contributes to the observed disc thickness: rapid changes in the orientation of the galactic plane mix the configuration of young stars. The frequently mentioned ‘upside-down’ formation scenario of galactic discs, which posits that young stars form in already thick discs at high redshift, may be missing this additional mechanism of quick disc inflation. The actual formation of stars within a fairly thin plane is consistent with the correspondingly flat configuration of dense molecular gas that fuels star formation.