The thread on Susan Boyner got me thinking “Who has done a leading role with no training and no experience?”
The only person I know of is Israel’s Dudu Fisher. He was trained as a cantor, tried out for Les Miserables after seeing it in London, and ended up with the lead role of Jean Valjean.
Anyone else who got to the top without years in the chorus?
I did, in a high school production of Charley’s Aunt. 
Lots of child actors could be said to have had a starring role their first time out - think of Willy Wonka and the Chocolate Factory, Old Yeller, Oliver and Paper Moon.
Does Cameron Diaz count? Her first movie role was in the Mask as the female lead opposite Jim Carrey. Carrey was definitely the “star” of the movie, but she was 2nd billing in her first movie out, which is pretty rare.
Mark Hamill comes to mind. Before starring as Luke Skywalker, he was an extra on one episode of Night Gallery, then voice acted in an animated post-apocalyptic science fiction/fantasy film, Wizards.
He was also in the pilot of Eight is Enough as David Bradford, but turned down the series to do Star Wars
Marlee Matlin won an Oscar for her film debut in Children of a Lesser God.
Jon Heder (Napoleon Dynamite)
Both Sean Astin (Rudy, Lord of the Rings) and Josh Brolin (No Country for Old Men, W.) made their silver screen debuts in the 1985 cult classic, The Goonies.
ETA: It was more of an ensemble cast, though.
What about Edward Norton:
started with:
Primal Fear
The People vs. Larry Flynt
Everyone Says I Love You
Rounders
American History X
Fight Club
Keeping the Faith
The Score
Death to Smoochy
then down the cast in Frida
followed by:
Red Dragon
25th Hour
The Italian Job
Down in the Valley
The Illusionist
Hamill was a featured actor in the TV show, The Texas Wheelers.
Jean Seberg’s first movie role was as Joan of Arc in Saint Joan.
Millie Perkins started out as the lead in Diary of Anne Frank.
Klinton Spillsbury’s first (and last) acting role was the lead in Legend of the Lone Ranger. All his lines had to be redubbed by another actor.
Christopher Charles Mintz-Plasse (McLovin from Superbad) auditioned on a whim. From Wiki, he didn’t even have any headshots - he simply took a picture of himself on his camera phone.
Eddie Furlong was found on the steps of the Pasadena Boy’s and Girl’s Club and put in Terminator 2.
In the 1995 American drama film, Kids, director Larry Clark cast New York City “street” kids with no previous acting experience in the film, notably Leo Fitzpatrick (Telly) and the late Justin Pierce (Casper). Some have faded back into relative obscurity; meanwhile, others, such as Rosario Dawson (Rent, Sin City, Men in Black II, Alexander) and Academy Award-nominee Chloë Sevigny (Boys Don’t Cry, American Psycho, Big Love, Party Monster), have since found success in their acting careers as well-recognized actresses. Jon Abrahams also continues acting and starred in a string of successful movies including The Faculty, Boston Public, Scary Movie, and Meet the Parents.
Hang S. Ngor. He was a doctor in Cambodia. He had no acting experience but plenty of life experience to play Dith Pran in The Killing Fields. Won an Oscar for his first acting role of any kind.
Ben Kingsley had extensive experience as an actor in theater and on British television, but I believe “Gandhi” was his first film role.
May I present one of the great trivia answers of all time: Klinton Spillsbury.
Exactly one show business credit, one starring role, never worked again.
I know of two, probably because I’m personally connected to both.
Kelly McGillis (an old friend of mine) starred in Reuben, Reuben. That was her true “debut” as far as film and television combined.
Meg Tilly did a couple of small TV bits before her film debut, which was directed by my then-brother-in-law, who also cast my sister in a small roll as a reporter in his own debut, “One Dark NIght”, which was named “Mausoleum” originally.
How could I have forgotten my favorite religious epic?
Pier Paolo Pasolini used a LOT of amateurs with little or no acting experience in his cast for “The Gospel According to St. Matthew,” including Enrigue Irazoqui, who played Jesus.
The credits of The Princess Bride say “Introducing Robin Wright,” although consulting imdb, she apparently was in a couple TV series prior to.
And while it’s hard to be the “star” in a cast that includes om Cruise and Jack Nicholson, Rob Reiner gave the role of the primary defendant in “A Few Good Men” to Wolfgang Bodison, a non-actor who’d been working as a production assistant.
Supposedly, Rob Reiner wasn’t happy with any of the auditioners, and said, “What we really need is somebody like Wolf here… say Wolf, have you ever done any acting?”