We utilize the Navier-Stokes equations to study the amplification of perturbations in a three-dimensional boundary layer subject to continuous stochastic forcing. The freestream conditions correspond to recent experiments conducted in the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT) under quiet flow for a unit Reynolds number of 9.9 × 106 m−1. We first compute the steady flowfield and demonstrate how the Mach number and shape of the leading edge shock produce three-dimensional flow features using inviscid arguments. We then show agreement with experiments where infrared (IR) imaging reveal numerous streamwise heat streaks. Next, we perform an unsteady forced numerical simulation to investigate perturbation growth in the boundary layer. Sparsity-promoting dynamic mode decomposition (SPDMD) is used to extract the dominant modes from the forced numerical simulation. Using SPDMD and wall pressure data, we identify four distinct mechanisms of perturbation growth. The available experimental data agrees with the extracted modes in terms of frequency content demonstrating the predictive capabilities of our forced ‘quiet DNS.’.