IMO, the best way to get faster is to ride with, and try to keep up with, people that are faster than you. Pay attention to your diet and hydration (so forth). You should start seeing results pretty quickly, such as within a couple of weeks you should note you are not AS far behind as you were. If you don't see that improvement, it can be an indicator that you are unable due to various factors.
Another aspect that is helpful is to ride as many different route/types as you can, as hard as you can. Riding in a group is typically better for results in my own experience. I don't (didn't) always push hard when I was by myself unless there was some goal, like another rider I wanted to catch or a race against time to a point.