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Context. The presence of [$α$/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] - [$α$/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 $α$-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.