Protecting them upfront is honestly where most people slip up. Get a good leather protectant spray - the silicone-based ones work better than anything else I've found - and hit your sneakers with it while they're still fresh out of the box. Let it dry completely, then do a second coat a few days later. After that, a quick wipe with a damp microfiber cloth once a week handles 90% of the dirt before it sets in. The protectant creates a barrier so stuff doesn't bond to the leather the way it would otherwise.
For actual cleaning when they do need it, I keep a soft brush and some leather cleaner on hand, but honestly you're only using it maybe once a month instead of every other week. The difference is night and day compared to throwing them on without any treatment first. White leather loves to look grimy fast, but that protective layer keeps it looking fresher way longer with minimal effort. Just avoid those rough scrub brushes and the aggressive cleaners - they wear through the leather faster than the dirt ever would.