Ultra-intense lasers that ionize atoms and accelerate electrons in solids to near the speed of light can lead to kinetic instabilities that alter the laser absorption and subsequent electron transport, isochoric heating, and ion acceleration. These instabilities can be difficult to characterize, but X-ray scattering at keV photon energies allows for their visualization with femtosecond temporal resolution on the few nanometer mesoscale. Here, we perform such experiment on laser-driven flat silicon membranes that shows the development of structure with a dominant scale of 60 nm in the plane of the laser axis and laser polarization, and 95 nm in the vertical direction with a growth rate faster than 0.1 fs⁻¹. Combining the XFEL experiments with simulations provides a complete picture of the structural evolution of ultra-fast laser-induced plasma density development, indicating the excitation of plasmons and a filamentation instability. Particle-in-cell simulations confirm that these signals are due to an oblique two-stream filamentation instability. These findings provide new insight into ultra-fast instability and heating processes in solids under extreme conditions at the nanometer level with possible implications for laser particle acceleration, inertial confinement fusion, and laboratory astrophysics.