In the opening or introduction to an essay, it is often a good idea to outline a line of argument or a thesis that you can then explore and debate during the main body of the essay. When trying to think about what that thesis could be, it is perhaps useful to think about the morals, messages, or ideas that you think the author might have been trying to convey.
Of Mice and Men is about the importance of companionship, kindness, and inclusivity. It is also about loneliness, cruelty, and alienation. Steinbeck explores all of these themes through the relationship between the two protagonists, George and Lennie. An interesting, or catchy, thesis pertaining to these characters and these themes could certainly make for an engaging opening of an essay.
For example, you might argue, in your opening paragraph, that through George and Lennie, Steinbeck presents the idea that companionship is an essential source of hope in an otherwise hopeless world. Indeed, the story is set during the Great Depression, and the world at this time, especially for itinerant workers like George and Lennie, would certainly have seemed rather hopeless. Their companionship is what sustains George and Lennie, at least momentarily.
For a possibly more contentious, arresting opening, you might also argue that Steinbeck presents the idea that human nature is more predisposed towards cruelty and selfishness than it is towards kindness and altruism, and that this cruelty and selfishness is exacerbated by difficult circumstances. The kindness between George and Lennie is an exception in the story. There is far more cruelty, selfishness, and persecution in the story, as evidenced by the treatment of outsider characters like Crooks, Curley's wife, and Candy. At the end of the story, the kindness demonstrated by George and Lennie is overwhelmed by the cruelty of Curley and the lynch mob he assembles to kill Lennie. Lennie's death is, arguably, symbolic of the better aspects of human nature being overwhelmed by the worst.