Large-eddy simulations of a Blasius boundary layer over a flat plate, without a leading edge, at multiple levels of incoming free stream turbulence are considered. The data from the saved snapshots are then applied to an input-output model where non-linear terms of the Navier-Stokes equations are treated as an external forcing. By separating the inputs corresponding to the perturbations coming through the inflow boundary and non-linear forcing, we can perform the full reconstruction of the statistics of the flow observed in the simulations and discriminate which frequencies and wavenumbers are more affected by either linear or non-linear dynamics. Different frequency-wavenumber combinations reveal streaks that grow predominantly through linear or non-linear mechanisms, the former occurring upstream and the latter at downstream stations of the boundary layer.