The phrase boy meets girl is used with reference to a conventional or idealised romance. It originated in cinematographic plot summaries in which boy meets girl featured.

The Oxford English Dictionary (3^rd edition, 2008) erroneously states that this phrase is posterior to Boy Meets Girl, a play by Bella Cohen Spewack (1899-1990) and Samuel Spewack (1899-1971), which was first performed in Philadelphia on 18^th November 1935. The following is from the review of this play, published in The Racine Journal-Times (Racine, Wisconsin) of Sunday 15^th December 1935:

It is a blithsome [sic] comedy of Hollywood in which the authors lay down a three-act barrage of good-natured ridicule of the nation’s art-manufacturing center.
Two irreverent scenarists are its chief characters. They are devoting themselves to concocting what the trade terms “horse operas” for a big-time studio.
But somehow they can’t take it seriously. They devise a formula for their high, dramaturgic task which is simplicity itself: “Boy meets girl—boy loses girl; boy wins girl.” And despite the prayers and wailing of high studio executives they proceed on this formula to turn out picture after picture.

I have, however, found earlier instances of the phrase boy meets girl. The earliest is from the column Behind the Scenes in Hollywood, by Harrison Carroll, published in The Shamokin Dispatch (Shamokin, Pennsylvania) of Tuesday 3^rd March 1931:

Harry Brand, who is a great time-saver, has invented a nine-word synopsis that will fit any film at any time.
“Boy meets girl — tear ’em apart — together for finish.”
How do they figure such things out?

The second-earliest instance is from The Screen Parade, in the Tampa Morning Tribune (Tampa, Florida) of Sunday 9^th July 1933:

“Boy Meets Girl” (tentative title), is a vehicle written for Dorothy Jordan and Joel McCrea by Vina Delmar.

As early as 1934, the American actress Constance Campbell Bennett (1904-65) regarded boy meets girl as denoting a type of trite romance, according to the Reading Times (Reading, Pennsylvania) of Tuesday 6^th February of that year:

Constance Bennett believes that the French farce offers producers of screen musicals an opportunity to get away from the banality of the boy-meets-girl plot that makes so many of them look like rubber stamp facsimiles of each other.
“Moulin Rouge,” her first starring picture for the Twentieth Century Pictures which is being released by United Artists as the feature film attraction at Loew’s sets a precedent in screen musicals which, she believes, will prove a fertile example.
Adapted from a Paris stage success, “Moulin Rouge” is no less concerned than other musicals with the motivating forces of love. But instead of “love at first sight” adventure between over-grown adolescents, it presents the battle of a young wife to win back the playwright husband whom she has driven into the arms of a French actress.

It is interesting to remark that, before it became a phrase, boy meets girl was almost a romantic cliché sometimes used in newspaper titles (in which the definite and indefinite articles are often omitted). For example, the following is the beginning of a story titled Romance Is Saved as Boy Meets Girl Starting Back Home, published in The Philadelphia Inquirer (Philadelphia, Pennsylvania) of Thursday 25^th January 1923:

National Park, N. J., Jan. 24.—A romance with all the denouements of a first-rate movie thriller, that left a Virginia girl penniless in Camden and appealing to the police for shelter, finally blossomed anew tonight when Miss Martha Bowles, of Meadow View, Va., and Robert Murray, Jr., of this place, were welcomed by Murray’s parents to their home on Simpson avenue near Red Bank avenue, Verga.