Until recently, Barkhad Abdi was doing shifts at his brother's Minnesota mobile-phone shop. Now the 28-year-old has acting plaudits coming out of his ears thanks to his turn as khat-chomping rookie pirate Muse in Captain Phillips, Paul Greengrass's retelling of the real-life 2009 hijack of the Maersk Alabama off the Somali coast. When we meet, he's just snatched the London Critics' Circle supporting actor gong from the jaws of Jared Leto and Michael Fassbender and, two weeks later, he scoops the same award at the Baftas.

But it's his Oscars nod that's proving most difficult to digest. "It is surreal, I would say," muses Abdi, sitting in his room at the hotel that hosted last night's ceremony, wearing an oversized suit and Nikes. "That was the one show that I used to watch." If he's victorious at the Hollywood backslap this weekend, it will be a historic win; for what makes his rapid rise all the more remarkable is that Captain Phillips is Abdi's acting debut.

"There was an open casting call on TV and I went," says Abdi. He's managing to look only vaguely weary despite recounting the inauspicious beginnings to his success story for what must be the millionth time. "They asked me easy questions – 'What's your name? 'Where were you born?' – and they assigned me to a character and gave me a script." After the open audition, targeted at Minneapolis's sizeable Somali community, Abdi's quietly authoritative presence won him the role of Muse, the pirate ringleader who wrangles with Tom Hanks's Phillips for control over the hefty American cargo ship. Three of his friends were cast as his cronies. "We auditioned together, we went home and we practised. We loved acting and we really wanted to get this."

Much has been made of Somali-born Abdi's previous life as a limousine driver in Minneapolis, where his family settled when he was a teenager; his story touted as that of the most unlikely zero-to-hero American dreamer. But Abdi wasn't a complete newcomer to the film-making process, previously jobbing as a director on Somali hip-hop videos. "I was working on my own film, too, but it never worked out," he says sheepishly. "When you work with a great director you realise you are far from being a director."

It was Greengrass, the British film-maker behind United 93 and The Bourne Supremacy, who both guided and relied heavily on Abdi during the Captain Phillips shoot, with the nuances in the novice's acting carrying much of the story. "[Paul] calmed me down. I remember on the first day, I was so nervous. He told me: 'Don't think about the whole movie, just think about today.'"

One bonus of his on-set anxiety was that Abdi could feed it back into the fragile resolve of his character. "[Muse] was feeling exactly the same way as I was feeling. When he got there [to the ship] he doesn't want to mess up, he doesn't want to celebrate early." That wasn't the only convenient parallel. Despite Hanks being a mentor of sorts to his co-star – "He tells me, career-wise, just use it wisely and work your hardest" – Abdi spends the film engaged in battle with the Hollywood heavyweight, both in terms of the story and screen presence. Greengrass purposely kept the two apart before their first scene in order to harness the real-life dynamic. "We'd never met, that was the hard part. I know who he is, but he doesn't know who I am. This guy is nobody and this guy is an Oscar winner. So it's just: 'Hey, I'm here.'" The need to assert himself over Hanks with the help of nothing more than swagger is what gives Abdi's performance such an edge.

Muse's sinister order to Phillips in that scene – "Look at me, I'm the captain now" – was an unscripted line that came "in the heat of the moment, because he wasn't talking to me, he was just talking, shutting me down." It's the first battle cry in the pair's hair-raising physical and mental skirmish and has become something approaching a catchphrase. "I never understood how big a line it was until the trailer came out and it kept getting bigger. Now everyone's saying it to me."

Yet it's Muse's vulnerability, rather than his aggression, on which the film's emotional and political impact hinges. The pirate's credulity regarding the US authorities' bogus ransom negotiations may make for a happy ending, but it's also the moment when America's superpower seems almost tragically all-consuming. Abdi says he tried to empathise with the naivety of the real Abduwali Muse (now doing 33 years in a US prison). "When he gets caught, the [news] footage of him smiling… It's different, someone crying and someone laughing. That shows you how he doesn't know what deep trouble he's in. That's how I see it, the ignorant part. He's happy about the cameras, he's smiling for them."

As a child, Abdi lived in Somalia amid the beginnings of civil unrest. But the forked path in his childhood, which could have resulted in a life not unlike his character's, apparently had no bearing on his preparation for the role. He bristles when I ask him if he was expected to bring any of his experiences of Somalian life to his character. "No, we never talked about that," he says quickly. "It was just all about the script." Which must make the treatment of him by some media as a spokesman for the Somali community especially odd, and a little daunting. "It is weird. A lot of people try to ask me political questions. I'm not a politician. There's not much I know about the exact politics of Somalia today." He hasn't been back to the country yet. Instead, he says his experiences of Somalia are just like everyone else's. "It's what I see on the internet, what I hear word of mouth. People don't have schools, they don't have jobs, there's no system; it's crazy to look at it and to imagine how you live in it. I feel truly blessed to survive that, get an education, and to understand what life really is about."

Abdi's future now looks dazzlingly bright, so much so that it's hard to envision what might come next. He's looking at scripts, he says, but goes on the offensive when I ask if he's worried about being typecast: "That [Muse] is not me. If that was exactly who I am then that would be scary." In the year's limbo-like hiatus between the film's wrap and its release, he went back to work in his brother's shop. "I remember when the film came out, a lot of people came to the store." To see him? "Yeah, so I couldn't work there any more." If that door has been closed, many in Hollywood are suddenly ajar, but for now Abdi remains remarkably level-headed about his newfound success.

"There might be other parts I'm better at, or this might be the best I get. I want to find out, I'm up for the adventure."

Captain Phillips is out on DVD and Blu-ray now