I don’t think there is a way to get a random time offset in CC Particle World. I think you would need to create multiple layers of the effect, with a different texture layer for each one with different start time animations.
Trapcodes Particular supports random start and looping capabilities for particles, and if you are really up for a challenge you might be able to do it with Particle Playground.
Johnny Cuevas, Editor
ThinkCK
“I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work.”
—THOMAS EDISON on inventing the light bulb.