The actin cytoskeleton has the unique capability of producing pushing forces at the leading edge of motile cells without the implication of molecular motors. This phenomenon has been ex- tensively studied theoretically, and molecular models, including the widely known Brownian ratchet, have been proposed. However, supporting experimental work is lacking, due in part to hardly accessible molecular length scales. We designed an experiment to directly probe the mechanism of force generation in a setup where a population of actin filaments grows against a load applied by magnetic microparticles. The filaments, arranged in stiff bundles by fascin, are constrained to point toward the applied load. In this protrusion-like geometry, we are able to directly measure the velocity of filament elongation and its dependence on force. Using numerical simulations, we provide evidence that our experimental data are consistent with a Brownian ratchet-based model. We further demonstrate the existence of a force regime far below stalling where the mechanical power transduced by the ratcheting filaments to the load is maximal. The actin machinery in migrating cells may tune the number of filaments at the leading edge to work in this force regime.