There's an option, firstPanelToLoad
which defaults to 1. You could generate a random number based on the amount of slides you have. If you have 4 slides, I think it would be something like:
firstPanelToLoad:(Math.floor(Math.random() * 4) + 1)
And send me an email if you get stuck. I'm the author of the Liquid Slider and don't mind helping out where I can.