No, you don't have to start your play with a premise. You can start with a character or an incident, or even a simple thought. This thought or incident grows, and the story slowly unfolds itself. You have time to find your premise in the mass of your material later. The important thing is to find it.
No two dramatists think or write alike. Ten thousand playwrights can take the same premise, as they have done since Shakespeare, and not one play will resemble the other except in the premise. Your knowledge, your understanding of human nature, and your imagination will take care of that.