What happens if you take the birth control pill before your period?
Nothing serious, but by starting it off cycle like that it can take an extra month before you can be sure that you are fully protected from pregnancy. During the interim maybe you are, and maybe you aren't.
As you should know, until you have gone through an entire cycle on BC pills you need to use condoms to guard against pregnancy. So if you start the pills before your period, you won't know when to start the clock to begin your "entire cycle on BC pills".
Best bet is to wait.