The Lambertian limit for solar cells is a benchmark for evaluating their efficiency. It has been shown that the performance of either extremely thick or extremely thin solar cells can be driven close to this limit by using an appropriate photon management. Here we show that this is likewise possible for realistic, practically relevant thin-film solar cells based on amorphous silicon. Most importantly, we achieve this goal by relying on random textures already incorporated into state-of-the-art superstrates; with the only subtlety that their topology has to be downscaled to typical feature sizes of about 100 nm.