Amid the humble Florida rapper’s croons and raps about life and pain, there’s a unique voice that’s starting to emerge. Lil Poppa probably wouldn’t mind if he didn’t get any more popular.

In 2007, at just 7 years old, Jacksonville, Fla. rapper Lil Poppa got his start in rap, writing music for his church under the tutelage of his older brother. By the time he was 10, he was rapping ...