I would say to non-believers: "Imagine the strongest pain you've ever experienced – for example, when you broke your leg or passed a kidney stone – and then consider that a period can hurt like that too".
During menstruation, the uterus should empty itself, the blood must have a free outlet, and some forms of exercise can make this difficult.
There is no single good time to talk to your daughter about her period. There are thousands of opportunities to do so.