It pays to actually check IMDb before posting. 
Cameron Diaz in The Mask fits the bill I think 
But Jeannie Linero who played bridesmaid Lucy Mancini. Only a couple credits after that.
Animal House debuts
Karen Allen: Katy
Martha Smith: Babs Jensen
Kevin Bacon: Chip Diller
Peter Reigert: Boon
Brad Dourif in One Flew Over the Cuckoo’s Nest.
According to IMDB, Robert Vaughn’s first film appearance was an uncredited part in The 10 Commandments.
As far as I can see, Mark Hamill’s first film was Star Wars – maybe some of his TV credits were made for TV movies. Do they count?
To be fair, The American Way was added to his IMDB entry pretty recently. Last time I looked up his entry, about two months ago, it wasn’t there.
Clint Eastwood debuted in “Revenge Of The Creature” which IMDB says was the highest grossing of the Creature From The Black Lagoon movies. Dunno how big of a “hit” it was but certainly a classic series.
Sylvester Stallone’s first film was either “Annie Hall” (like Jeff Goldblum he played a thug) or you could consider that quickie porn flick he did which certainly made a lot of money and was well-publicized when word got out in the 1980s(?).
Speaking of Stallone, Hulk Hogan’s movie debut was in Rocky 3 which did quite well.
And speaking of Annie Hall, that was Sigourney Weaver’s film debut.
Kevin Bacon in Animal House, along with Karen Allen. ETA, 5timechamp said it first.
Jenette Goldstein in Aliens.
I think it’s pretty easy to keep coming up with names, seems like a lot of folks got noticed in a big movie and that’s how they were able to get their start and keep getting credits.
The American Way in '62 was probably an cheap indie-non-hollywood film, so I think the Godfather counts. A short but dazzling career, five movies, only one not receiving best picture, turns out that is The Conversation.
Jamie Lee Curtis had bit parts in popular TV shows (such as Qunicy), but her first movie credit was certainly a big hit: Halloween.
I think many of the cast members of the SNL earliest IMDB credits are SNL.
It looks like Nicolas Cage and Anthony Edwards made their film debuts in Fast Times at Ridgemont High.
Furthermore, according to IMDB The American Way has a run time of 10 minutes http://www.imdb.com/title/tt0447603/maindetails. I wouldn’t consider a 10 minute film a theatrical release.
Hmm- if you throw out The American Way every movie in which John Cazale appeared either won
Godfather I & II
The Deer Hunter
or nominated for
The Conversation
Dog Day Afternoon
the Academy Award for Best Picture.
Another thread made me look up the career of Andrew Robinson, and he merits mention in this thread. One TV guest spot, and then the killer, Scorpio, in Dirty Harry.