Searches of the Google Books and Elephind (newspaper) databases yields more than a dozen matches for cleavage (in the revealing physique sense) from the year 1946, a couple of which date directly or indirectly to August 4, 1946—one day earlier than the August 5 Time magazine article cited in the posted question and in TaliesinMerlin's excellent answer.
Here is the full text of "'Wicked Lady' Too Wicked: Scenes Reshot for America," in the [Sydney, New South Wales] Truth (August 4, 1946):
NEW YORK, Saturday.—British producers are resentfully reshooting several costly scenes of 'The Wicked Lady' because Hollywood's self-imposed censorship considers actresses' half-covered bosoms far more sexy than yards of uncovered legs.
'The Wicked Lady', is only one of three films which will have to be altered to meet the Johnson Office morality code.
It is a very interesting example of the length to which the American film industry goes to keep half-baked censors like the unofficial League of Decency out of its hair.
'The Wicked Lady' is a film of the Restoration period, and beauteous Margaret Lockwood and Patricia Roc wear low-cut, half-bosom-exposing costumes which, according to Joe Breen, United States interpreter of the Hollywood morality code, now in London, 'expose too much cleavage.'
'Cleavage' is Hollywood's own delicate term for the shadowed depression dividing an actress's bosom.
English-produced 'The Rake's Progress' will have its title changed to 'The Notorious Gentleman' before American distributors show it.
Mr. Breen fears that the American public would think from the title that it was a documentary film on gardening.
And from a brief item in Newsweek (August [?] 1946) [combined snippets]:
Amazed: Prof. Cyril E. M. Joad, of London University and author of "A Guide to Modern Wickedness," denounced the censoring of motion pictures in the United States and said he was amazed at American insistence upon banning the "cleavage . . . the top end of the little ravine that runs down between and separates women's breasts. In an article in The London Sunday Dispatch on Aug. 4, he also complained that American films bar the words "damn" and "bastard," and asked: "Does nobody in America ever swear and are there no illegitimate children?"
Since Newsweek claims to be quoting comments by Professor Joad that were first reported in an article published in the London Sunday Dispatch of August 4, 1946, the latter source would seem to have a nominal one-day advantage over the August 5, 1946, issue Time magazine—but as Sydney is several time zones ahead of London, the Truth may have an even stronger claim to having the earliest published occurrence of the term in the relevant sense.
From Earl Wilson's column in the Los Angeles [California] Daily News (August 13, 1946):
Look! There's Diana Lynn, beautiful young Paramount actress, wearing a low-cut white dress that shows much cleavage.
"Diana, why are you so un-dressed-up tonight?" I ask her.
Earl Wilson was a smart-alecky, gossipy, night-life journalist who wrote a nationally syndicated column for decades, operating out of New York City and based at the New York Post. I remember that he was still going strong (and his column was still appearing regularly in my hometown newspaper, the Houston Post) in the late 1970s.
From Mary Armitage, "Liaison Lack on Movie Morality," in the [Adelaide, South Australia] Mail (August 31, 1946):
Forty scenes of Gainsborough's "Wicked Lady" have been reshot at a cost of L5,000, and a great number of man-hours, because America's production code censor, Joseph I. Breen, decided that Margaret Lockwood's period gowns were too low-cut to be seen by American audiences.
This is not the first time that a British movie has been rejected by America through "chest trouble," or what film people call "cleavage." The same thing happened over the release of the British-made "Scarlet Pimpernel." American production code officials then considered Merle Oberon's eighteenth century gowns were too revealing for twentieth century American audiences.
From "Here She's Wicked; Here She Isn't" in the [Sydney, New South Wales] Daily Telegraph (September 15, 1946):
U.S. film censors were upset by the "cleavage" in the low-bosomed gowns, of Margaret Lockwood in the British film, The Wicked Lady (left), and of the supporting actress, Patricia Roc.
They demanded the re-shooting of 40 close-ups before passing the film for the American public.
From "Josephine O'Neill's Reviews," in the same issue of [Sydney, New South Wales] Daily Telegraph
A more dashing leading man than Russell Wade could have made this fleeting frivol [The Bamboo Blonde] more fun. But Russell is a Sad Sack of a hero; and Miss [Frances] Langford, in spite of that blonde hair, and those cleavage gowns, is oddly prim.
From Earl Wilson's column in the Los Angeles [California] Daily News (September 27, 1946):
Ginger Rogers shows excess "cleavage" In "Magnificent Doll" and the Johnston office insists on covering her ...
From "'Breast Line' War Is Now On: British-U.S. Battle Front,"in the [Sydney, New South Wales] Sun (October 20, 1946):
Another British film held up here [in Hollywood] by censorship trouble is "Pink String and Sealing Wax."
Breen's office is objecting to the "cleavage" shown by Googie Withers' evening gowns.
From "Royalty Censored a Wedding Gown," in the [Sydney, New South Wales] Daily Telegraph (October 27, 1946):
A "cleavage" had become a matter of concern to the Ladies of the Royal Household.
At Buckingham Palace, Her Majesty Queen Elizabeth and the two Princesses held strong opinions about the propriety of the wedding gown chosen by their cousin, 22-year-old Patricia Edwina Victoria Mountbatten.
This week she was marrying 21-year-old John Ulick Knatchbull, seventh Baron Brabourne.
It was a beautiful gown of beaten gold Indian brocade. It had been designed in Paris by the famous couturier Captain Edward Molyneux. So had the blue bridesmaids' frocks.
That was the trouble. They were all "too, too Parisian" for the Regal taste, too daringly cut, and exposed rather too much bosom.
On the dresses at they stood, a Royal veto was placed. Like the costumes in the movie, "Wicked Lady," they had to be remade.
From "Movie Censorship: It Confuses British Movie Makers but U.S. Producers Get Around It," in Life magazine (October 28, 1946):
The thing that annoys British film-makers most about the [U.S.] Production Code is the highly legalistic way it works, especially regarding sex. To remove any symptom of sex from the traditional symbol of a happy marriage, a double bed is never shown on the screen except with only one person in it. "Indecent exposure" is prohibited, but any bathing suit passes so long as it has a high bodice. "Cleavage" is banned, but a tight sweater is permissible (see top picture, opposite [of Diana Lynn in The Bride Wore Boots]). Brutality and drunkenness are prohibited except "when essential to the plot." Very often producers insist that such things are essential. ...
...
[Caption:] Cleavage between women's breasts forced revision of forthcoming British historical movie The Wicked Lady, starring Patricia Roc (above). For U.S., distributors had to substitute close-up shots for revealing ones like this.
From "US Censors Were Snubbed," in the [Sydney, New South Wales] Daily Telegraph (November 10, 1946):
LONDON, Sat.—British censors gave a subtle snub to their US fellows this week.
That Howard Hughes-Jane Russell film, The Outlaw, came up for review.
American censors banned the film for over three years, passed it, and then clamped down the ban again.
Reason: The "cleavage" in the bosomy shots of the heroine, Jane Russell.
The British film censors saw The Outlaw, and, after asking for one tiny cut, passed it for General Exhibition.
From Earl Wilson's column in the Los Angeles [California] Daily News (November 23, 1946):
NEW YORK.—Paulette Godard now wears a frog in her bust.
I guess I'd better clarify that.
When Ingrid Bergman was upsetting Broadway at the opening of the stage show "Joan of Lorraine"—which dumb showgirl Taffy Tuttle calls "Joan of Fontaine"—there sat practical Paulette wearing this wee gold frog hanging down in what the English would call her "cleavage."
"Look!" said Paulette to me, superfluously.
From an unidentified item in Negro Digest (1946) [combined snippets]:
. . . Nudist magazine, Sunshine & Health, court-testing Post Office department's ban on nude white breasts but okay of nude Negro breasts. Which reminds of longstanding N. Y. state film censorship rule which allows movies to expose Negro women's breasts full view but turns thumbs down on just a wee too much cleavage on white girls . . .
From Gordon Gilmour, "London Diary: Ernest Bevin May Be on His Way Out," in the [Sydney, New South Wales] Sun (December 4, 1946):
Critics argue that to spend £17,000.000 a year on films like the currently-showing, much-panned "The Outlaw" is throwing money down the sink—an action which not even Jane Russell's ample "cleavage" can justify.
And from a caption accompanying "London Letter: A Night at Picadilly's Beau Geste Club," in the [Hobart, Tasmania] Mercury (December 17, 1946):
New Cleavage Necklines: These two pastel-shaded afternoon frocks by Frederick Starke show you the cleavage necklines and elaborately draped bodices that are the very newest things in London. The one on the left is in pink, and a further feature to note is the heart-shaped bodice. The frock on the right is in dove grey.
Conclusions
The use of cleavage to refer to a certain kind of physiological negative space seems to have arisen in the U.S. movie industry in connection with the Motion Picture Production Code of 1934 and its latter-day enforcers.
The earliest cited mentions of cleavage in this sense seems to have come from three different periodicals on three different continents within a day of each other: an article in a Sydney newspaper on August 4, 1946; an article in a London newspaper on the same day; and an article in a U.S. news weekly dated August 5, 1946. (Note that the third instance may actually have come out earliest, depending on whether Time magazine was already engaged in the misleading practice of dating its periodicals by their sell-by date—the date when they get pulled from newsstands—rather than their actual first day on sale.)
All three articles focus on the fallout from a decision by U.S. censors to ban a British film (The Wicked Lady) for exposing too much of the actresses' skin, leading the studio to reshoot numerous close-ups—at considerable additional expense—after making wardrobe adjustments to placate the censors. Given that Joe Breen of the U.S. Production Code Administration had, according to the August 5 Time magazine account, been in London "for the past fortnight" making his case for banning the film, British newspapers may have been exposed to (and reported on) the term cleavage as early as late July 1946.
In this regard it is noteworthy that, whereas the August 5 U.S. and August 4 Australian articles referring to cleavage focus on Joe Breen, the August 4 London article quotes to it in an interview with Professor Cyril Joad, whose familiarity with the term may well have resulted from his having encountered it in an earlier article in the British press. If I had an subscription to the British Newspaper Archive, I would check its collection from July and early August 1946 for possible earlier mentions of cleavage—but I don't.
All three of the August 4 and 5 articles noted above treat the term cleavage as contemporaneous jargon among U.S. film industry executives and censors—but I haven't found any evidence that the term had appeared in the press or in published books prior to August 4, 1946. Mention of cleavage in the relevant sense in a private letter that one U.S. Production Code executive sent to another in 1935 (as cited by TaliesinMerlin) offers persuasive evidence that the expression was in use within the film industry more than a decade earlier, but there is no reason to suppose that it had escaped that narrow zone of use before Breen's visit to London in the summer of 1946.
Although the initial flurry of articles about the Wicked Lady kerfuffle undoubtedly played a major role in propagating the term, other sources subsequently helped spread it beyond the context of film industry censorship. In the United States, one such source was the widely read syndicated columnist and bon vivant Earl Wilson, who used the term three times in columns published in the second half of 1946. Curiously, in the last of those three columns, Wilson presents cleavage as a British English term, presumably because he picked up on it (as so many others did) in the wake of the Wicked Lady controversy.
That British English speakers were, from a fairly early date, familiar with the term outside the context of film industry usage is evident from the commercial appearance of garments with "cleavage necklines" in England in late 1946—a fashion development that an Australian newspaper characterizes as "the very newest things in London."
In Australia, early mentions of cleavage in the relevant sense are peculiarly concentrated in Sydney newspapers, with instances unrelated to the film industry appearing as early as October 1946.