Understanding how super-massive black holes form and grow in the early Universe has become a major challenge1,2 since it was discovered that luminous quasars existed only 700 million years after the Big Bang3,4. Simulations indicate an evolutionary sequence of dust-reddened quasars emerging from heavily dust-obscured starbursts that then transition to unobscured luminous quasars by expelling gas and dust5. Although the last phase has been identified out to a redshift of 7.6 (ref. 6), a transitioning quasar has not been found at similar redshifts owing to their faintness at optical and near-infrared wavelengths. Here we report observations of an ultraviolet compact object, GNz7q, associated with a dust-enshrouded starburst at a redshift of 7.1899 ± 0.0005. The host galaxy is more luminous in dust emission than any other known object at this epoch, forming 1,600 solar masses of stars per year within a central radius of 480 parsec. A red point source in the far-ultraviolet is identified in deep, high-resolution imaging and slitless spectroscopy. GNz7q is extremely faint in X-rays, which indicates the emergence of a uniquely ultraviolet compact star-forming region or a Compton-thick super-Eddington black-hole accretion disk at the dusty starburst core. In the latter case, the observed properties are consistent with predictions from cosmological simulations7 and suggest that GNz7q is an antecedent to unobscured luminous quasars at later epochs.