  The high abundance of disc galaxies without a large central bulge challenges
predictions of current hydrodynamic simulations of galaxy formation. We aim to
shed light on the formation of these objects by studying the redshift and mass
dependence of their intrinsic 3D shape distributions in the COSMOS galaxy
survey below redshift $z=1.0$. This distribution is inferred from the observed
distribution of 2D shapes, using a reconstruction method which we test using
hydrodynamic simulations. Our tests reveal a moderate bias for the inferred
average disc circularity and relative thickness, but a large bias on the
dispersion of these quantities. Applying the reconstruction method on COSMOS
data, we find variations of the average disc circularity and relative thickness
with redshift of around $\sim1\%$ and $\sim10\%$ respectively, which is
comparable to the error estimates on these quantities. The average relative
disc thickness shows a significant mass dependence which can be accounted for
by the scaling of disc radius with galaxy mass. We conclude that our data
provides no evidence for a strong dependence of the average circularity and
absolute thickness of disc-dominated galaxies on redshift and mass that is
significant with respect to the statistical uncertainties in our analysis.
These findings are expected in the absence of disruptive merging or feedback
events that would affect galaxy shapes. They hence support a scenario where
present-day discs form early ($z>1.0$) and subsequently undergo a tranquil
evolution in isolation. However, more data and a better understanding of
systematics are needed to reaffirm our results.
