To rise from amateur status to a position in the UFC, it'll take 2-8 years. If you have UFC connections and/or train at a high-profile gym, you can get there quicker. No matter what, maintain a strong work ethic and a winning record to boost your progress through the ranks.
Becoming a UFC fighter at the age of 20 with no experience would be a challenging and ambitious goal. The first step would be to start training in mixed martial arts (MMA) and various fighting disciplines such as Brazilian Jiu-Jitsu, Muay Thai, wrestling, and boxing.