Active turbulence describes a flow regime that is erratic, and yet endowed with a characteristic length scale. It arises in animate soft-matter systems as diverse as bacterial baths , cell tissues and reconstituted cytoskeletal preparations. However, the way that these turbulent dynamics emerge in active systems has so far evaded experimental scrutiny. Here we unveil a direct route to active nematic turbulence by demonstrating that, for radially aligned unconfined textures, the characteristic length scale emerges at the early stages of the instability. We resolve two-dimensional distortions of a microtubule-based extensile system in space and time, and show that they can be characterized in terms of a growth rate that exhibits quadratic dependence on a dominant wavenumber. This wavelength selection mechanism is justified on the basis of a continuum model for an active nematic including viscous coupling to the adjacent fluid phase. Our findings are in line with the classical pattern-formation studies in non-active systems, bettering our understanding of the principles of active self-organization, and providing potential perspectives for the control of biological fluids.