I am an official licensee of Krav Maga Worldwide, a sanctioned organization of krav maga. I own and operate two schools in my area & have been teaching for close to 10 years, but I am not a black belt in krav maga. I am what they rank as Expert III/IV in black belt preparation and will have up to 2 more years before qualifying to test for black belt.
When I began, I was already a higher level student & entered what we call Phase training in LA, at their nat. training headquarters. This consists of 7 days of physical, mental, and teaching type of training with a final phase testing. Having previous krav maga training, I went through the program at an accelerated pace but still had to do each phase & then enter Expert & do each of them passing each test.
As far as your question, you can definitely become an instructor in krav maga in three years, but you will not be a black belt nor the nor the best instructor you can be. On average, it takes 5 to 7 years to test for a black belt in krav maga (by US standards as opposed to Israeli standards when I started my krav maga training in NYC).