Recent advances in bolometric detector technology have allowed submillimetre (submm) wavelength measurements to contribute important data to some of the most challenging questions in observational cosmology. The availability of large-format filled-array cameras during the next decade, however, promises to provide far-infrared (FIR) to millimetre (mm) observations with unprecedented imaging fidelity. The simultaneous increase in the telescope collecting area of new facilities, and their location at ground-based sites with the highest atmospheric transmission will provide observational data with greater sensitivity and resolution. With the opening of the Italian/French Concordia station at Dome C in Antarctica there is now an exciting opportunity to make unique FIR–submm wavelength observations (200–850 μm) through atmospheric windows that are almost open to space. The development of submm astronomy from Dome-C, undertaken with a phased-programme of increasingly larger telescopes, will make critical observations of the high-redshift universe. In particular, we argue that a long-term strategy for Dome C should include plans to construct a 30-m telescope with a large field-of-view (≥0.1 sq deg), designed and optimized to operate at ~200 μm. With such a single-dish facility it will be possible to resolve 100% of the population of galaxies that contribute to the integrated FIR-submm extragalactic background. In this paper we describe how a large-aperture submm telescope at Dome C will provide unique data to address fundamental questions and killer science regarding the evolutionary history, nature and large-scale distribution of the population of high-redshift optically-obscured starburst galaxies