See the answer to the FAQ on how often people promote as it is relevant.
A very general answer might be anywhere from 3 - 5 years to reach 1st Dan or 1st Degree Black Belt but this depends on attitude, discipline and attendance.
At Enso Center, we like to focus on learning correct technique at all levels.
The 1st Dan Black Belt is an important milestone in your journey within martial arts but it is also only just a milestone.