Neuronal growth cones sense a variety of cues including chemical and mechanical ones to establish functional connections during nervous system development. Substrate-cytoskeletal coupling is an established model for adhesion-mediated growth cone advance; however, the detailed molecular and biophysical mechanisms underlying the mechanosensing and mechanotransduction process remain unclear. Here, we adapted a motor-clutch model to better understand the changes in clutch and cytoskeletal dynamics, traction forces, and substrate deformation when a growth cone interacts with adhesive substrates of different stiffnesses. Model parameters were optimized using experimental data from Aplysia growth cones probed with force-calibrated glass microneedles. We included a reinforcement mechanism at both motor and clutch level. Furthermore, we added a threshold for retrograde F-actin flow that indicates when the growth cone is strongly coupled to the substrate. Our modeling results are in strong agreement with experimental data with respect to the substrate deformation and the latency time after which substrate-cytoskeletal coupling is strong enough for the growth cone to advance. Our simulations show that it takes the shortest time to achieve strong coupling when substrate stiffness was low at 4 pN/nm. Taken together, these results suggest that Aplysia growth cones respond faster and more efficiently to soft than stiff substrates.