Spectral index distributions ordered following the spatial and time evolution of dust in star- and planet-forming environments. (i) α in the submillimetre (< 350 GHz) for the diffuse ISM (grey dotted representative distribution from Planck Collaboration Int. XIV 2014); (ii) at 1–3.1 mm for the protostellar envelopes at 500 au scales from this work and G19 combined (violet); (iii) at 1–3.1 mm for the class 0 protoplanetary disks from this work and G19 combined (green); (iv) for typical class II disks at 1–3.1 mm (green dash-dotted line, Tazzari et al. 2021). We also show the spectral indices reported by Bracco et al. (2017) for prestellar cores (blue box), class 0 YSOs (red/orange boxes), and a T Tauri disk (green box), all within a common filament in Taurus. The spectral indices of protostellar envelopes appear to be bridging the gap between ISM and disks, hints to a continuous evolution of dust properties from one to the other. On the right, a sketch represents the evolution of dust that emerges from the spectral indices variations, with growth from the (sub-)micron grains in the ISM to the mm/cm-sized grains of disks, through infalling envelopes. The typical scales and values are the ones of the aforementioned studies.