I find the easiest way to jump start a new filter is to use the new tank as the cleaning bucket for one of my existing filters. Since I have 26 tanks running right now, it is never a problem finding a filter that needs cleaning. Often I will use the new tank to clean 2 or 3 filters while the new filter is running the whole time. When I then fishless cycle the tank, it is not unusual to find it fully cycled in less than a week.
The cleaning bucket approach to cycling works well but be aware that it means you will need to clean the new filter fairly soon and the substrate will need a gravel vac before you add in the fish.