The mutual trapping and locking of intense fundamental and second-harmonic continuous-wave light beams propagating in bulk crystals with large second-order nonlinearities is investigated. We report the outcome of a comprehensive series of numerical experiments to study the dynamics of the excitation of solitons with Gaussian input beams under different material and excitation conditions in terms of input powers, wave-vector mismatch, and linear walk-off between the fundamental and the second-harmonic waves. We show the dynamics of the mutual trapping and study how solitons emerge from the input beams in a wide variety of conditions that are not necessarily close to those given by stationary solutions of the governing equations. Solitons also emerge with inputs that fall far from those solutions. We specifically investigate the dynamics of soliton excitation with only the fundamental beam at the input face of the nonlinear crystal and in configurations with a moderately large phase mismatch. We find large oscillations in the amplitude of the beams with potentially important implications. We also study the mutual dragging of the beams in the presence of linear walk-off and in particular of phase-matching geometries with a nonsmall, but moderate, walk-off.