By 1952, Marlon Brando was well on his way in Hollywood, with three remarkable roles under his belt: his big-screen debut as a paraplegic war vet in The Men; a searing on-screen reprisal of his Broadway turn as the iconic brute Stanley Kowalski in director Elia Kazan’s A Streetcar Named Desire; and the title role in the biopic, Viva Zapata!, about the Mexican revolutionary hero.

But for all those successes, Brando had not yet made the cover of LIFE — a magazine that prided itself on capturing and reflecting the nations’ obsessions and interests, week after week after week. In 1952, that oversight was remedied, as legendary photographer Margaret Bourke-White shot a portrait session with Brando, capturing the 28-year-old star in a casual, playful mood.

For reasons lost to time, Bourke-White’s photos — discovered in LIFE’s archives and marked with the sole descriptive phrase, “cover tries” — were never published in the magazine. (Though Bourke-White’s portraits never saw the light of day, Brando ultimately did grace the cover of LIFE, making his first appearance in character as Antony from Julius Caesar in the April 20, 1953, issue. He’d appear on the cover three more times.)

Here, meet the young Brando at his most charismatic and mysterious, seen through the lens of one of LIFE’s greatest photographers, in a series of photos that never ran in the magazine.

Liz Ronk, who edited this gallery, is the Photo Editor for LIFE.com. Follow her on Twitter @lizabethronk.

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