We analysed a set of very metal-poor stars, for which accurate chemical abundances have been obtained as part of the ESO Large Program 'First stars' in the light of the Gaia DR2 data. The kinematics and orbital properties of the stars in the sample show they probably belong to the thick disc, partially heated to halo kinematics, and to the accreted Gaia Sausage-Enceladus satellite. The continuity of these properties with stars at both higher ([Fe/H] > −2) and lower metallicities ([Fe/H] < −4.) suggests that the Galaxy at [Fe/H] −0.5 and down to at least [Fe/H] ∼ −6 is dominated by these two populations. In particular, we show that the disc extends continuously from [Fe/H] ≤ −4 (where stars with disc-like kinematics have recently been discovered) up to [Fe/H] ≥ −2, the metallicity regime of the Galactic thick disc. An 'ultra metal-poor thick disc' does indeed exist, constituting the extremely metal-poor tail of the canonical Galactic thick disc, and extending the latter from [Fe/H] ∼ −0.5 up to the most metal-poor stars discovered in the Galaxy to date. These results suggest that the disc may be the main, and possibly the only, stellar population that has formed in the Galaxy at these metallicities. This would mean that the dissipative collapse that led to the formation of the old Galactic disc must have been extremely fast. We also discuss these results in the light of recent simulation efforts made to reproduce the first stages of Milky Way-type galaxies. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programmes 165.N-0276(A) (P.I.: R. Cayrel).