Starting with "Normal"
Still working with the concept that life is normal until the precipitating incident (PE), the other logical place to start is with the normal life. That means starting the book before the PE.
For example, in The Princess Diaries, the PE is when the main character finds out she's a princess. But the book starts with the main character's normal life, and the learn-she's-a-princess scene doesn't start until page 26 (trade).
I CAN'T BELIEVE SHE'S DOING THIS TO ME!
Like everybody doesn't already think I'm a freak.
How much more of a freak could I be?
Oh, God, if you really do exist, please don't let them find out about this.
So out of TWO MILLION guys, she has to go out with Mr. Gianini.
(Meg Cabot, Princess Diaries)
Probably the best reason for starting with normal life is to provide context for the PE. Without context all scenes are less interesting. If the author wants the PE to be as interesting as possible, the book will usually start with normal life.
Learining she is a princess is intrinsically interesting and could have been the start of The Princess Diaries. But that scene had more awesomenesss potential than any other event in the book, and a big part of the awesomeness is a normal teenager suddenly discovering she is a princess. So, to realize the potential of that scene, she first has to be portrayed as normal.
In Mr. Mercedes (King), the PE is the retired detective getting a letter from a mass murderer. But King wants the reader to feel the evilness of the mass murderer. So, the first scene ends with the mass murderer driving his car into a crowd of people.
King could have started the book there – that would have been natural; most authors would have. A mass murder is high in intrinsic interest. But King knows that to feel the horror, the reader has to empathize with at least one of the people being murdered.
So that book starts with a most ordinary event – Auggie, a normal guy, is out of work and attending a job fair. We read about him, then about him talking to a mother with her young child. And only then are they murdered.
The description of normal life can also be one-half of a contrast: Normal life and then something happens. Contrast is not the most exciting thing a writer creates, but it's nice.
Cabot created nice contrast in her description of normal life: The popular kids ignored her, she has no control over her life, one of her interests is her cat, the doorman wouldn't let her in, etc. The exact opposite of being a princess (though of course she then must deal with being both).
Starting with Setting
In a way, starting with normal life is a, well, normal way to start a book. It's just usually done with description – the main character's life is described, then the PE is told.
Starting with action makes it more natural to start with the actual PE. The rest of this section is about starting with life as normal, because that's a little trickier.