Does starting birth control on "day 1" help with the pain of that week's menstrual cycle?

I’ve read that birth control pills help with painful cycles.
I’m supposed to start taking the pill either today (day 1 start) or Sunday (Sunday start). I’m in pretty severe pain from cramps stomach and back pain and pressure, nausea, dizziness.
Would starting the pill today instead of Sunday ease my cramps during this period, or would it be too soon?