The challenge is now, can we end with 0 cards in deck AND 0 cards in the supply?
If it's possible, it would be tough.
The game ends if 3 piles are empty. At the very least there are 17 piles (10 Kingdom, 3 treasures, 3 VP, Curse). You can empty 2 and then have 1 card left in 15 piles.
To have 0 cards in Supply you'll need to empty them all on the last turn. But to have 0 cards in your Deck as well, you'd need to trash them all on the same turn you gain them. I believe this is impossible.
You can't buy them. The only way to trash cards as you buy them is with Watchtower (or I suppose Trader when Silvers are out), but then you have at least Watchtower in your hand (and you would also have whatever cards are in play that enable you to buy 15 things).
You can't easily gain them either, because then you have to PLAY gainers. You'd have to use a self-trashing gainer, i.e. Feast or BoM-as-Feast.
This is roadblock already. I don't think there is a way to gain the last Province with a self-trasher. You'd need cost reducers in play, and in play means not trashed.
Looking past that, how would you trash gained cards anyway? You can't use a regular trasher because then it ends up in play. Watchtower maybe? But then how do you trash the Watchtower afterwards without leaving something in play?
I don't think it's possible. But maybe I'm overlooking something.