Based on quantitative results on quantum observables in a Planckian regime, I will argue that using dynamical lattices `a la CDT to construct and explore the nonperturbative path integral over Lorentzian geometries is a bona-fide quantum field-theoretic "method" rather than an "approach" to quantum gravity. Its most important features are universality, unitarity and the presence of powerful numerical tools to directly simulate and measure a chunk of quantum spacetime of about 20 Planck lengths across. This small observational window is a preferred place to look for clues to what quantum gravity is all about. Despite the diffeomorphism-invariant and nonlocal character of the observables, qualitatively new and surprising UV properties have already been discovered, and compatibility checks with semiclassical expectations for several cosmological observables ("classical limit") have been performed successfully. The underlying new mathematics is that of random geometry and beyond-Riemannian geometry.