There is a saying I really like: "I may not have hope, but I do have determination". I'm not sure who said it, but it's true (for some things).
People have faced many hopeless tasks and triumphed. They only seem inevitable after the fact. I'm sure it was difficult to expect the end of racism in South Africa, but it happened. It's not hard to think of many other examples.
It's worth it to start working on a cause you believe in, and other people will join.