Do a man and a woman have to oragasm at the same time in order to conceive?

No. The woman doesn't even have to have an orgasm at all. The man has to release sperm into the vagina, and the sperm have to reach the egg in the woman's uterus. The egg is there if she has ovulated and it has lodged properly in the lining of the uterus. Orgasm has nothing to do with it.

If the egg isn't fertilized while it is in the uterus, the uterine lining breaks down and passes out of the body, and that's her period. Then you have to wait for another cycle before conception becomes possible again.