To add to what /u/The_Alaskan said, while the digital age had made it much easier to watch foreign films than sixty years ago (or even twenty!), there were outlets for the distribution for foreign films in American theaters and, increasingly, television, in the 1950s and 60s. American movie studios like Columbia maintained departments to but the American distribution rights for non-American films and could often acquire them relatively cheaply. Small time production companies also found that acquiring foreign products was a means to keep in the black. This gave American studios additional products to fill various markets and sell to theater chains and television channels. The market for foreign film imports grew in the 1950s and 60s in the wake of the Supreme Court's ruling that US film studios could not own their own theaters. This, and the pressures from television, meant the studios focused more on big budget productions and less on B-pictures; foreign imports fill in this gap. In the case of Japan, Toho also maintained its own theater in Los Angeles and opened its own theaters in larger markets like New York and San Francisco. In these cases, the large Japanese-American population of the West Coast and the Bohemian New York audiences provided an audience for these films.

Part of the reason for US studios to acquire the rights for these now classic foreign movies was prestige, but other, less noble, motives were at play. Advertising for foreign films played up the exoticism and allegedly alien culture on display. This twisted the export market so that Japanese historical epics or Kaiju films were more likely to be aired while serious films in a contemporary setting were sometimes ignored. Aside from unprofessional dubbing, US distributors often butchered films for reasons of length. In the case of the Seven Samurai, Columbia cut some fifty minutes of the film, including most of the scenes with the Japanese peasants. Visconti's masterpiece The Leopard was similarly cut for length to be more palatable to American's allegedly short attention span.

The American distributors also zeroed in on the stereotypes of European and Asian libidinousness to sell these films as socially acceptable dirty films. Because of the loophole in US censorship laws, foreign films evaded many of the censors that restricted American films. The transgressiveness of the Italian neorealists like De Sica or the French New Wave attacked many bourgeois values, but American advertisements foregrounded these films' assaults on sexual propriety. One of the US taglines for And God created woman was "but the Devil invented Bridgette Bardot." While this was a translation of the original French tagline, it was more prominent in US advertisements. Bardot herself became marketed as a European sex kitten in The Naughty Girl with taglines like "the BEST THING that has happened to French movies since I cannot remember when...artistically and materially." One of the more egregious case of this sexualized advertising was Kurosawa's touching film Ikiru. In this film, a soulless Japanese bureaucrat learns he has terminal cancer and after a night of wild abandonment at a strip club decides to do something worthy with his life and build a children's park. The US posters for this touching and humanistic film neither feature the bureaucrat, nor the park, nor any other character from the film except the Japanese stripper. The US distributor for Ikiru, Brandon Films, got some free publicity over the initial brief detainment of the film's print by US custom officials for lewdness and advertised "See it now! Complete! Uncut!" and "Go Now- Lest you Repent Later!"

However flawed this system of distribution was and despite its compromising of the artistic integrity of these films, they were a visible enough presence within the cinematic community to have an impact. The 1970s turn to directorial auteurs like Francis Ford Coppola, many of whom were fans of filmmakers like Kurosawa, created a pressure to bring these films over in uncut and subtitled form. Coppola's post-Godfather clout would be instrumental in ensuring that Kurosawa's later films would make it to US screens. The decline in theater ticket revenues meant that art house films, while very small compared to the bigger picture, were one guaranteed source of revenue. Although less foreign films were on American screens than in their 1960s heyday, they were now screened uncut and with subtitles.

But the biggest game-changer for the consumption of foreign films was the advent of home-video. Not only did it lower the cost of bringing over foreign films, the nascent home video market mushroomed in the late 1970s and 80s and foreign/art house film sections for home rental became a standard part of many video stores. Furthermore, various specialty stores like Kino International and Facets Video mushroomed that could cater to art house patrons through their own brick and mortar shops and mail order.

The first mention of Seven Samurai in the New York Times is a June 6, 1954 piece by Ray Falk, who posted a dispatch from the South East Asia Film Festival. It was published on the fifth page of the Sunday issue's arts section. He wrote in part:

"'Seven Samurai' statistics are staggering in themselves. The film's running time is three and a half hours, much too long for the plot. Mr. Kurosawa could have told his story just as well in half the time, but his intense desire to recreate life rather than create an illusion has as in his past pictures got in the way of his cutting-room scissors."

After the movie picked up awards at the Venice Film Festival in fall 1954, Paramount picked up its American distribution rights in August 1955. It didn't open in New York City until November 19, 1956, when it opened at the Guild Theatre under the title The Magnificent Seven. In a piece explaining the "Eastern Western," Bosley Crowther explains that "Mr. Kurosawa is telling a story that has been told a hundred times (or maybe more) in a setting of sagebrush and with sheriffs instead of samurai."

Four years later, after the "Eastern Western" turned into a "Western Western" with the release of John Sturges' The Magnificent Seven, there was a surge of interest in that film's inspiration.

The 1960s brought a surge of interest in films and filmmaking, especially beyond the mainstream. The New York Film Festival began in 1962, and in its third edition (in 1965), Kurosawa's Red Beard was touted as one of the top attractions. Crowther, who had nine years before attended the premiere of The Magnificent Seven, pronounced Red Beard to be cliche and "a burst of boredom."

Edit: One year later, in 1966, there was a spinoff of The Magnificent Seven, which contributed to a story in which the cultural pundits expressed alarm at the pace of remakes in Hollywood.