I have also had this problem several times with my 2012 Impreza Sport (CVT). I've taken it to my dealer twice and both times they say they can't replicate it and therefore nothing was done.
In addition to the slow start, sometimes after the slow start I get the following message on the LCD
"The vehicle dynamics control system needs to be checked".
If I turn off the vehicle and start again the car starts fine and the error is gone.