  Context. The presence of [$\alpha$/Fe]-[Fe/H] bi-modality in the Milky Way
disc has animated the Galactic archaeology community since more than two
decades. Aims. Our goal is to investigate the chemical, temporal, and
kinematical structure of the Galactic discs using abundances, kinematics, and
ages derived self-consistently with the new Bayesian framework SAPP. Methods.
We employ the public Gaia-ESO spectra, as well as Gaia EDR3 astrometry and
photometry. Stellar parameters and chemical abundances are determined for 13
426 stars using NLTE models of synthetic spectra. Ages are derived for a
sub-sample of 2 898 stars, including subgiants and main-sequence stars. The
sample probes a large range of Galactocentric radii, $\sim$ 3 to 12 kpc, and
extends out of the disc plane to $\pm$ 2 kpc. Results. Our new data confirm the
known bi-modality in the [Fe/H] - [$\alpha$/Fe] space, which is often viewed as
the manifestation of the chemical thin and thick discs. The over-densities
significantly overlap in metallicity, age, and kinematics, and none of these is
a sufficient criterion for distinguishing between the two disc populations.
Different from previous studies, we find that the $\alpha$-poor disc population
has a very extended [Fe/H] distribution and contains $\sim$ 20$\%$ old stars
with ages of up to $\sim$ 11 Gyr. Conclusions. Our results suggest that the
Galactic thin disc was in place early, at look-back times corresponding to
redshifts z $\sim$ 2 or more. At ages $\sim$ 9 to 11 Gyr, the two disc
structures shared a period of co-evolution. Our data can be understood within
the clumpy disc formation scenario that does not require a pre-existing thick
disc to initiate a formation of the thin disc. We anticipate that a similar
evolution can be realised in cosmological simulations of galaxy formation.
