I often rant against 1× drive trains for how unsatisfactory they are for road+MTB use, and particularly those 10-teeth sprockets are simply a bit rubbish.
But they're definitely not that bad either. The 10-50t SRAM GX cassette on my enduro bike lasted perhaps 1500 km, a lot of it in the small sprockets, no problem. (I would probably have kept it a lot longer still if I hadn't replaced the entire rear wheel.) And I don't think Shimano SLX is much worse, 320 km really should be nothing for it.
So if that sprocket is in fact worn out already, there must be something else wrong. As the other answers said, riding with a very dirty chain is an obvious explanation – but that's actually something I'm also often guilty of, and again it hasn't shortened the life of my cassette like that.
What I'd strongly suspect instead is that the cassette is not dead yet, or at least wasnt killed purely by the distance of road riding. You didn't say in the question how you've came to the conclusion that it's worn out, but presumably you mean it doesn't properly shift into that gear and/or keeps skipping when riding in it? Well, that can have multiple reasons other than being worn out.
- A dirty, rusty or worn chain will always shift worse and be more prone to skipping. And a 10-tooth sprocket makes it particular hard because the chain needs to bend around such a tight radius, so even if the other gears still work it can still be all the fault of the chain.
- A slightly misaligned or stuck derailleur can obviously cause these problems easily too, and again it is common that this surfaces first in bad performance on the outermost sprockets.
- As I said, 10-tooth sprockets are generally a bit rubbish. Even in prime condition they aren't really suitable for putting a lot of power down, but only as a “highway gear” for cruising along or for gaining a little extra speed on a down slope. If you regularly used this gear for out-of-the-saddle sprints, then I'm not surprised you would get chain skip.
Even if one of these were the original problem, then it is very possible that repeated skipping and/or bad shifts have by now destroyed the cassette. So one takeaway is: heed the symptoms early on – don't punish a drivetrain that starts to behave badly with brute force, instead get down to the underlying cause immediately and treat it.
And generally treat a cassette as the delicate thing that it is. I often hear MTB riders mercilessly crunching through gear shifts to the point that I almost feel bodily pain. Don't do that. Decent quality sprockets can withstand big power and last a long time if you treat them well. Always reduce the load under upshifts or multi-gear downshifts (single gear downshifts on a steep climb are ok under full load). And if you ride at strong power, use big enough cogs, at least 12 teeth. Yes, if you want to keep that riding style then that may mean you need a bigger chainring, but I'm not sure it really makes sense to ride this way.