Anywhere from about 4-5 years to infinity. Actually, the only way 4 years would happen would be if you enlisted with a degree and somehow magically got picked up for OCS almost immediately. The problem is that someone enlisted with a bachelors in the Army comes in as an E-4, not an E-1.
There is no 'promotion' from enlisted ranks to officer ranks. Most people that enlist with never be commissioned, and therefore never be a captain. On the other hand someone could do a couple of years and get picked up for a commissioning program, the length of which could depend on how much college they have left to do. Or, they could do 10 or more years, knock out a degree part time, and get picked up for OCS.
So, in short, even if someone enlisted and got picked up for a commissioning program, there is no specified timeline for making captain, other than the timeline that starts from the day they are commissioned.