Erase
Purchase a Mr. Clean Magic Eraser (or your store’s knockoff). These sponges are the greatest invention since the stripper pole.
Cut the sponge into 2-inch strips (you’ll get more use out of them, since using a whole sponge dirties it fast), apply a little bit of water and rub like crazy on anything vinyl. You’ll be shocked at how much dirt you can remove, especially from the sneaker’s lower sides.