Begin With Recounting an Experience
Another way of beginning an essay would be to begin with recounting of an experience directly, which takes the reader to the core thought or phenomenon which you plan to analyze through an essay. If you are talking about animal rights, recount your first experience of seeing an animal being butchered and what impression it left upon you. If you are talking about gender equality, start with recounting an experience which was a clear example of male chauvinism.