We utilize the externally forced linearized Navier-Stokes equations to study the receptivity of pre-transitional boundary layers to persistent stochastic excitation sources. In contrast to the widely used resolvent analysis that quantifies amplification mechanisms associated with input-output pairs of identical temporal frequency, our approach determines the steady-state response to white-in-time excitation. Stochastic forcing is used to model the effect of free-stream turbulence that enters at various wall-normal locations and the fluctuation dynamics are studied from locally parallel and global perspectives. In addition to forcing with trivial (identity) covariance, we utilize the spatial spectrum of homogeneous isotropic turbulence to model the effect of free-stream turbulence. Global flow analysis predicts the amplification of a cascade of streamwise scales throughout the streamwise domain. Even though parallel flow analysis does not account for the effect of the spatially evolving base flow, we demonstrate that it captures important trends and prevailing length-scales. Our study offers a systematic, computationally efficient framework for quantifying the influence of free-stream turbulence on the dynamics of velocity fluctuations in weakly non-parallel flows.