There are stories that come to mind almost fully delineated: the characters, what happened, and how it ended. But most writers say this is the exception.
I've had stories materialize two ways: a character that started taking to me, or a plot that only needed its main actors revealed. Speaking for myself only, most of my stories began with a plot. Most of the writers I know personally have told me theirs began with a character.
Examples from my writing life of a plot-first story: I pass a house and sense that something ominous happened there, and then know what it was. I can barely breathe thinking about the powerful events. Now I need to find out who was there to tell about it.
Example of a character-first story: I can see and almost hear this girl, Holly. Nothing ever goes right for Holly, yet she always comes out on top with her slightly dented dignity intact. I've only met Holly in my imagination, but I let her tell me of her many adventures, and, boy, can she tell a story.
I’ll let the master storyteller of them all say it, as he said it best:
Their names are What and Why and When and How and Where and Who.