Borderline impossible. The menstrual cycle just doesn't work that way. Women are fertile for about five days of the month: the day they ovulate and about four days before because that's as long as sperm can survive in the uterus. Menstruation occurs 12-14 days after ovulation on average. The period between ovulation and menstruation the luteal phase. A luteal phase shorter than 10 days is rare and usually requires fertility treatment if the woman wants to get pregnant because it may not be enough time for the egg to implant itself in the uterine wall. By the time a woman starts to get PMS symptoms, unless she has a ridiculously short luteal phase, she's a good week plus away from her last fertile day.

Tl;dr Unless there's something really weird going on with her cycle, a woman will not be fertile anywhere close to the start of her period.