  We use photometric metallicity estimates for about 700000 stars in the
surroundings of the Sun, with very accurate distances and 3-D motions measures
from Gaia DR3, to explore the properties of the metal-poor (-2.0<[Fe/H]<= -1.5;
MP) and very metal-poor ([Fe/H]<= -2.0; VMP) stars with disc kinematics in the
sample. We confirm the presence of a significant fraction of MP and VMP stars
with disc-like orbits and that prograde orbits are prevalent among them, with
prograde to retrograde ratio P/R ~3. We highlight for the first time a
statistically significant difference in the distribution of the Z-component of
the angular momentum (L_Z) and orbital eccentricity between prograde and
retrograde disc-like MP stars. The same kind of difference is found also in the
VMP subsample, albeit at a much lower level of statistical significance, likely
due to the small sample size. We show that prograde disc-like MP and VMP stars
display an additional component of the |L_Z| distribution with respect to their
retrograde counterpart. This component is at higher |L_Z| with respect to the
main peak of the distribution, possibly hinting at the presence of a pristine
prograde disc in the Milky Way. This hypothesis is supported by the results of
the analysis of a large sub-sample dominated by stars born in-situ. Also in
this case the prevalence of prograde stars is clearly detected at [Fe/H]<= -1.5
and their |L_Z| distribution is more skewed toward high |L_Z| values than their
retrograde counterpart. This suggests that the seed of what will eventually
evolve into the main disc components of the Milky Way may have been already in
place in the earliest phases of the Galaxy assembly.
