High-energy neutrinos propagating over cosmological distances are the ideal messenger particle for astrophysical phenomena, but the neutrino landscape above 10 PeV is currently completely uncharted. At these extreme energies and the frugal flux expected, the dominant experimental strategy is to detect radiofrequency emissions from particle cascades produced by neutrinos interacting in the vast polar ice sheets. The Radio Neutrino Observatory in Greenland (RNO-G) is an array of radio antennas embedded in the ice near Summit Station, currently being deployed. At completion, RNO-G will consist of 35 autonomous antenna stations distributed over $\mathcal{O}(50\,\mathrm{km}^2)$, making it the largest and most sensitive in-ice neutrino telescope with unique access to the northern sky. This article describes the design of RNO-G, outlines the calibration and simulation strategies developed, and summarizes first results based on the dataset collected by the first seven operating stations.