The boundary-layer transition on a generic hypersonic forebody at Mach 6 downstream of a sonic wall injection is investigated by means of implicit large-eddy simulation, Fourier analysis, and dynamic mode decomposition of numerical data. An academic Mach 4.2 flat-plate configuration with boundary-layer edge conditions matching those of the forebody is considered. Two empirical correlations are proposed to predict the penetration of the underexpanded tripping jet into the boundary layer (that is, the Mach disk height) as a function of the pressure ratio. Different transition mechanisms are observed downstream of the injection port, depending on the jet penetration. The dynamic mode decomposition reveals the spatial structures, temporal frequencies, and growth rates of three-dimensional instability modes. These modes, arising from the jet counter-rotating vortices, are either varicose or sinusoidal, with the latter being more efficient than the former for tripping the boundary layer at low-injection pressure. Recent experiments in the Boeing/U.S. Air Force Office of Scientific Research Mach 6 quiet tunnel at Purdue University show similar transition patterns, but also some discrepancies. A more representative configuration including crossflow effects, and more resolved simulations, is needed for a quantitative comparison.