I have many pairs of white shoes and I wear them frequently. They’re workhorses, and I want them to look polished and new. I wipe them down after every wear so that they look clean, crisp, and to prevent dirt from building up. Some of my more casual shoes have white soles, which I can’t get clean after just a wipe. They do, however, scrub extremely clean with Oxiclean powder, water, and a scrubbing sponge. That requires some elbow grease, and time for the shoes to dry because they get quite wet. Hands down this is most effective way to keep white soles sparkling white.
But if you’re in a rush and want clean white soles fast — use a Magic Eraser to clean them. Wet the eraser, scrub the soles quite vigorously, and Bob’s your uncle. I do find that the eraser disintegrates as you’re using it, and it leaves eraser crumbs on the soles. But they brush right off, and the process isn’t as much of a production as my Oxiclean method. Plus you can wear the shoes right away because they aren’t that wet.