I put my fingernail against the roll parallel to the edge of the tape and run it around the roll until I feel the edge.  (You could also use a knife blade.)  If all else fails you could make a tiny cut with a knife to create a new end, but this will result in some tape wastage.  (By the way, I find that using a paperclip or something similar between the roll and the end of the tape works pretty wel--better than folding over the edge, which leaves you with a flap when you use the tape.)  The other option is to buy a holder like you get for cellophane tape, but I've never seen one that hols the packing tape rolls you get in dollar stores.

I have a desktop packing tape dispenser that helps avoid that problem. I picked it up at one of the office supply stores years ago.

But if my tape does roll back up, I can usually find the end if I hold the roll up to a bright light. If I can't find the end or I'm really impatient, I take a scissors and cut through the first layer of the roll, then try to unravel it and find the end (this only works if you unravel it in the same direction the tape is running - you have a 50/50 chance). I usually ended up wasting a big wad of tape doing this, which is why I bought the desktop dispenser.