Context. The formation of the Galactic disc is an enthusiastically debated issue. Numerous studies and models seek to identify the dominant physical process(es) that shaped its observed properties; for example, satellite accretion, starburst, quenching, gas infall, and stellar radial migration. Aims. Taking advantage of the improved coverage of the inner Milky Way provided by the SDSS DR16 APOGEE catalogue and of the ages published in the APOGEE-AstroNN Value Added Catalogue (VAC), we examined the radial evolution of the chemical and age properties of the Galactic stellar disc with the aim of better constraining its formation. Methods. Using a sample of 199 307 giant stars with precise APOGEE abundances and APOGEE-AstroNN ages, selected in a ±2 kpc layer around the galactic plane, we assessed the dependency as a function of guiding radius of (i) the median metallicity, (ii) the ridge lines of the [Fe/H] − [Mg/Fe] and age–[Mg/Fe] distributions, and (iii) the age distribution function (ADF). Results. The giant star sample allows us to probe the radial behaviour of the Galactic disc from Rg = 0 to 14−16 kpc. The thick disc [Fe/H] − [Mg/Fe] ridge lines follow closely grouped parallel paths, supporting the idea that the thick disc did form from a well-mixed medium. However, the ridge lines present a small drift in [Mg/Fe], which decreases with increasing guiding radius. At sub-solar metallicity, the intermediate and outer thin disc [Fe/H] − [Mg/Fe] ridge lines follow parallel sequences shifted to lower metallicity as the guiding radius increases. We interpret this pattern as the signature of a dilution of the interstellar medium from Rg ∼ 6 kpc to the outskirts of the disc, which occurred before the onset of the thin disc formation. The APOGEE-AstroNN VAC provides stellar ages for statistically significant samples of thin disc stars from the Galactic centre up to Rg ∼ 14 kpc. An important result provided by this dataset is that the thin disc presents evidence of an inside-out formation up to Rg ∼ 10 − 12 kpc. Moreover, about ∼7 Gyr ago, the [Mg/Fe] ratio in the outer thin disc (Rg > 10 kpc) was higher by about ∼0.03−0.05 dex than in the more internal regions of the thin disc. This could be the fossil record of a pollution of the outer disc gas reservoir by the thick disc during its starburst phase.