Babayev joined Dynamo Football Academy in 2014 from FC Khimki, where he made his first steps in football. In five years Ulvi scored 48 goals for Dynamo Academy through the Club League summer tournaments.

In March 2020, the forward played his debut game in the YFL-1. In the fall he became one of the key players of the white-blue team, scoring 13 goals and making 10 assists in 23 matches of the YFL-2. At the same time, Ulvi started performing for the White-Blues’ team at the M-League.

This season, 17-year-old Babayev is a regular for Dynamo in the M-League (15 matches, 6 goals, 1 assist). He also takes part in Dynamo-2 and first team training sessions. On September 30, Ulvi made his debut for the second team against Znamya Truda (by now, he played 4 matches in the FNL-2).