What was Kudou Shinichi's first case? At what time? How old?/How big? What episode?

286~288 new york incident of Kudo Shinichi

tells that Shinichi and Lan went to L.A. to see Shinichi's mother, and the cinema met someone from a dark organization, and an actor was shot dead, so they didn't tell me the method. Then they met someone who plagiarized women with silver hair, who was also disguised as a dark organization, and met Akai Shuuichi.