I don't know how it all ends

I'm currently developing the novel idea. It's a rich and detailed world with unique and interesting characters, a fascinating backstory, and a very real, very imminent conflict.

The world is about to end. I know that much. I know why it's about to end. I know what events would, in a tragedy, cause the end of all (human) life on the planet.

I know that my protagonist and her companion are going to stop it. I have no idea how. None. Not even a "well, this might work." Nothing.

I've never been here before. Do people really start writing in this predicament? Have you ever written a story that you have no idea what the ending is? How do you deal with plotting? With figuring out what resources/knowledge/abilities your protagonist has to get to the ending?
But seriously? No idea how they're going to save the world.