Born in Zagreb, Croatia, Dukić says that as a child he enjoyed telling stories and was keen to express himself visually, so—not finding painting, writing or theater "dynamic" enough—he became interested in filmmaking and made many amateur short films as a teenager. His 1991 short film Mirta uči statistiku ("Myrtha Learns Statistics") and his 1992 short documentary Posebni gosti ("Special Guests") screened at Croatian film festivals, the latter winning the Oktavijan Award for Best Short Film from the Days of Croatian Film. He attended the Academy of Dramatic Arts in Zagreb, graduating with a Bachelor of Arts degree in film, later completing a Master of Fine Arts at the American Film Institute Conservatory in Hollywood, California in the United States.