You can use special floor leveling compounds that are made to go on thin 1/4 - 1/2 inch. They're reasonably tough.
I've been using High Performance Cement by Quikrete Self-Leveling Floor resurfacer from Lowe's to fix some bad bird baths on my slab. It's $39 for 50 lbs. It can be quite thin (< 1/4 inch) and is rated to be a wear surface. You need to mix it 4+ minutes with a paddle mixer and you need to prime the cement that you're sticking it to with a bonding agent.
I've also tried RapidSet Cement-All from Home Depot. It's "only" $24 for 55 lbs. It's not self leveling but if you add enough RapidSet Flow Control (or similar plasticizer) it gets close. Flow Control is about $3 a package and, IIRC, you can use up to 4 packages per bag of mix. It claims just to need a good pressure washing to get it to bond but I've had mixed results, especially in less than 1/2 inch thickness. If you use this, you really, really, have to keep it wet until it cures - otherwise it just peels and makes a mess.
Both of these products have really short working times - they say 20 minutes but I think 12-15 minutes is more like it.
If your floor is reasonably level, you were to make a dam around the area you want the pad, that's say a half inch tall and use the self leveling floor resurfacer it should work for you. I'd screed it off (even though they say you don't need to).
If you trip over the edge too much you can grind the edge down with a angle grinder and a diamond cup wheel.