If you get posted to a very, VERY busy ship, you could get it in a couple of years. From everything I've been hearing, in order to sustain the fleet and promote more force-generation in our sailors, the model of the 5-7 month deployments will be moved to 2-3 month mini-deployments.
Realistically, it took me about 3 years after my trades training, 1 Op CARIBBE (2 months), a 4-week work ups program, and a 7-month deployment on Op REASSURANCE in order to get my days, so it can be done, but it really depends on what trade you get and how much sailing you do.