Models of core accretion assume that in the radiative zones of accreting gas envelopes, radiation diffuses. But super-Earths/sub-Neptunes (1-4 R-circle plus, 2-20M(circle plus)) point to formation conditions that are optically thin: their modest gas masses are accreted from short-lived and gas-poor nebulae reminiscent of the transparent cavities of transitional discs. Planetary atmospheres born in such environments can be optically thin to both incident starlight and internally generated thermal radiation. We construct time-dependent models of such atmospheres, showing that super-Earths/sub-Neptunes can accrete their similar to 1 per cent-by-mass gas envelopes, and super-puffs/sub-Saturns their similar to 20 per cent-by-mass envelopes, over a wide range of nebular depletion histories requiring no fine tuning. Although nascent atmospheres can exhibit stratospheric temperature inversions affected by atomic Fe and various oxides that absorb strongly at visible wavelengths, the rate of gas accretion remains controlled by the radiative-convective boundary (rcb) at much greater pressures. For dusty envelopes, the temperature at the rcb T-rcb similar or equal to 2500 K is still set by H-2 dissociation; for dust-depleted envelopes, T-rcb tracks the temperature of the visible or thermal photosphere, whichever is deeper, out to at least similar to 5 au. The rate of envelope growth remains largely unchanged between the old radiative diffusion models and the new optically thin models, reinforcing how robustly super-Earths form as part of the endgame chapter in disc evolution.