Conflict in a story is like the match that starts a fire. When that match strikes is left up to the storyteller.
The number one lesson I've learned from writing, reading, workshops, conferences, teaching--you name it I've done it--is this: conflict should happen early and often. Most writers present conflict in the first chapter, some writers unveil it on the first page. But there are a few writers, admired and neglected, obscure and renowned, who weave conflict into the first sentence. First sentence!
Check out these opening sentences brimming with conflict.
"I found him in the garage on a Sunday afternoon." --Skellig, by David Almond
"I was thirteen when my dad caught me with Tommy Webber in the back of Tommy's Buick, parked next to the old Chart House down in Montara at eleven o'clock on a Tuesday night." --Story of a Girl, by Sara Zarr
"That morning, after he discovered the tiger, Rob went and stood under the Kentucky Star Motel sign and waited for the school bus just like it was any other day." --The Tiger Rising, by Kate DiCamillo
"He began his new life standing up, surrounded by cold darkness and stale, dusty air." The Maze Runner, by James Dashner
"It was almost December, and Jonas was beginning to be frightened." The Giver, by Lois Lowry
Not only are these sentences laced with conflict, but the authors' voices are apparent. These openings set the story in motion right away. Some of these writers pull back after the first sentence, but the conflict--the catalyst--is in motion. The fire has started, but there's gallons of more gas to throw on it. In traditional story structure this is known as the inciting incident--the event that ignites the story. This event always confronts the main character with some degree of conflict and sets the real story in motion.
Name for WAY-up-front-conflict:
Inciting Incident. Fire Starter.