If a 13 y/o has ovarian cysts, is it a sign that she will start her period soon?

Not necessarily: Ovarian cyst are not a natural part of menstruation. This does not tell us if a menstrual cycle will come. Ovarian cyst can cause irregular cycles.

It's not a sign: Prepubertal girls can have cysts, so it's not a sign of pending menses/menarche. Most women start their menses before age 14 in the U.S. There is also a condition called polycystic ovary syndrome, in which case one of the symptoms is lack of menses/period and small cysts. Talk to her pediatrician if you are concerned about this, especially if she is overwt, has high cholesterol or blood sugars.