We used photometric metallicity estimates for about 700 000 stars in the surroundings of the Sun, with very accurate distances and 3D 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 a prograde-to-retrograde ratio of P/R ∼ 3. We highlight a statistically significant difference in the distribution of the Z component of the angular momentum (LZ) and orbital eccentricity between prograde and retrograde disc-like MP stars for the first time. The same kind of difference is found in the VMP sub-sample, 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 |LZ| distribution with respect to their retrograde counterpart. This component is at higher |LZ| 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. In this case, the prevalence of prograde stars is also clearly detected at [Fe/H] ≤ −1.5, and their |LZ| distribution is more skewed toward high |LZ| 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 already been in place in the earliest phases of the Galaxy assembly.