Luminous hot stars (M_Ks_~8000K) dominate the stellar energy input to the interstellar medium (ISM) throughout cosmological time, are used as laboratories to test theories of stellar evolution and multiplicity, and serve as luminous tracers of star formation in the Milky Way and other galaxies. Massive stars occupy well-defined loci in colour-colour and colour-magnitude spaces, enabling selection based on the combination of Gaia EDR3 astrometry and photometry and 2MASS photometry, even in the presence of substantive dust extinction. In this paper we devise an all-sky sample of such luminous OBA-type stars, which was designed to be complete rather than very pure, providing targets for spectroscopic follow-up with the SDSS-V survey. To estimate the purity and completeness of our catalogue, we derive stellar parameters for the stars in common with LAMOST DR6 and we compare the sample to other O and B-type star catalogues. We estimate `astro-kinematic' distances by combining parallaxes and proper motions with a model for the expected velocity and density distribution of young stars; we show that this adds useful constraints on the distances and therefore luminosities of the stars. With these distances we map the spatial distribution of a more stringently selected subsample across the Galactic disc, and find it to be highly structured, with distinct over- and under-densities. The most evident over-densities can be associated with the presumed spiral arms of the Milky Way, in particular the Sagittarius-Carina and Scutum-Centaurus arms. Yet, the spatial picture of the Milky Way's young disc structure emerging in this study is complex, and suggests that most young stars in our Galaxy (t_age_