The Lost alum and current Hawaii Five-0 star is achieving a personal and professional dream on Tuesday as he steps into the shoes of The King of Siam in Broadway's The King and I.
Kim, 47, takes over for Ken Wantanabe (who received a 2015 Tony nomination for his performance in the revival) and has been dreaming of a role like this since he attended New York University's Graduate Acting Program.
"When you're a young acting student thinking about what success will look like, a big part of that would be being able to do a lead role at Lincoln Center and being on Broadway," tells PEOPLE. "I'm really fortunate that I can say, 'Here I am.' "
"One of the reasons I'm playing this role is because it's one of two plays in the musical theater canon that were designed with an Asian male in mind," says Kim, who is an outspoken advocate of diversity in Hollywood. "It's The King and I and Miss Saigon. There aren't others."
He continues, "So even though it's difficult for me to fit into my schedule, I knew I had to jump at this chance because it's Lincoln Center, it's [director] Bartlett Sher and I didn't know when this train was going to come around again."
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Kim calls growing numbers of projects that showcase "ethnically correct casting" – including The King and I and NBC's The Wiz Live! – a victory for representation in entertainment. He also acknowledges and appreciates that he's getting a chance on the boards for which he is still fighting on screen.
"I wonder if I'll ever be able to play a romantic lead in a movie, not because I don't think I could – I would love to – but because will anyone ever take a chance on me?" he says. To remedy that problem, he created 3AD.
He adds, "We're making strides. I'm not trying to say that every role needs to be [cast simply for diversity's sake], but there just needs to be a reflection of the culture we live in. I believe we can entertain while at the same time reflecting the America that I see, that I live in and that my friends live in."
Kim is appearing in The King and I at Lincoln Center's Vivian Beaumont Theater through June 26.