Bruh Kh1 is playable
What's the quickest possible draw?
Depends what planet you're on.
If White flags, as suggested, the chess game is over, in which case, I suppose, you could regard Kh1 or K anywhere on the board as "playable" because you're not any longer playing chess.

two legal moves one by each side then one side offer a draw, now only a draw if the other side accepts
Sam Loyd published a book of unusual chess problems and puzzles. As I recall, he published the shortest possible game that ends in stalemate and the shortest possible stalemate in which there are no captures. Both are much shorter than one would predict. I don’t have the games in front of me but you might look them up. Interesting and fun.

Sam Loyd published a book of unusual chess problems and puzzles. As I recall, he published the shortest possible game that ends in stalemate and the shortest possible stalemate in which there are no captures. Both are much shorter than one would predict. I don’t have the games in front of me but you might look them up. Interesting and fun.
Here's a blog that covers the topic. Shortest games to stalemate and ‘Mr. Robot’ chess scene.
Fun fact: Someone else before Sam Loyd discovered the 12-move capture-free game.
The players agree on a draw before the game.
it is not possible to do that until the game has started
On the contrary, it's rumoured to have happened quite often.
In some tournaments players are not allowed to agree a draw before move 30. But what if they repeat a position 5 times? They agree to nothing and claim nothing but still it is a draw
Would the arbiter force you to take your last move back and replace it with the only (and losing) alternative?