Gravity and pressure will prime a carto with time.
I like to keep my centre hole free of
juice is possible, i find my cartos will last longer this way.
I drip juice in from the top, with my carto on an angle and rotating before each drop. I'll do 3 or 4 drops then let it sit for a few mins, sometimes giving it a flick to speed to soaking time up. I'll also tank my cartos before ive filled them up, so the juice in the tank will also help fill it.
Whole process can take up to 30mins but by then you know its well and truly soaked and ready to go. There is no need for extra priming methods.