Simon Cowell (Getty Images)
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Simon Cowell nearly missed out — twice — on the chance to discover “X Factor” singing sensation Carly Rose Sonenclar.
The Westchester teen — who has been in first place for much of the competition — says she was only permitted to audition in front of the judges after another act dropped out at the last minute.
“I was an alternate,” she tells The Post.
Carly, 13, submitted herself to producers through a recording kiosk inside Paramus Mall in April.
“They came back to me a couple of weeks later and said I had to go to Providence the next morning — but I may not ever get seen,” she remembers.
The middle-schooler, who drew rave reviews on Broadway in “Les Misérables,” eventually earned a spot on a team coached by Britney Spears.
“The way she is kind of shy and then she gets on stage . . . she reminds me a lot of me, when I was younger,” the pop princess says.
“She is so cool. She just has this demeanor about her that she just gets it and she understands the business.”
Carly is one of four contestants remaining in the competition, and will perform two songs during tonight’s live episode at 8.
“I don’t believe you’re a human being,” Cowell — who is both a producer and judge — raved after one recent performance. “You can’t [sing like] that at 13.”
But producers of Cowell’s other competition, “America’s Got Talent,” were not as impressed when Carly auditioned for them as part of a duo in early 2012.
She performed Alicia Keys’ “Empire State of Mind,” with schoolmate Reed Peterson accompanying on piano.
“I don’t know what happened,” the teen says. “I thought we did great. Everything happens for a reason.”
Carly, who began singing at age 2, says she’s gotten used to rejection after years of cut-throat theater tryouts.
“Obviously, you get turned down more than you get picked,” she says. “I always forget about the audition the day after.”
Reality television, Carly says, was a way to set herself apart from the rest of the hopefuls in the New York theatre world.
“Stuff like [‘X Factor’] doesn’t happen on its own for people,” she says.
“There are people on Broadway right now who are so talented, but if you came out here to Hollywood, nobody would know their name. I now, from doing this, am more known than they are.”