  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 isolated galaxies with
stellar mass $M_* = 10^7 - 10^{10} M_{\odot}$ 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 $z_{1/2}$ ~ 0.1 kpc and
short-to-long axis ratio $z_{1/2}/x_{1/2}$ ~ 0.15. Disc thickness increases
with the age of stellar population, reaching median $z_{1/2}$ ~ 0.8 kpc and
$z_{1/2}/x_{1/2}$ ~ 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.
