Every contraceptive method has it's own effectiveness date.
Each gyno will have a plan for you as to when to start your birth control pills when first getting started on pills. "Sunday" start means that you run out of your 28 day pill pack on Saturdays, and that may be efficient for many women, but not so efficient for others. Especially if you just got your prescription and missed your Sunday start, yet you are wanting to be protected against pregnancy as soon as possible. So gynos have long been recommending "quick starts" meaning, start your pills as soon as you can, regardless of where you are in your cycle.
Once you have begun the pill within that first week of the cycle, and then taken 7 days of pills, you are protected against pregnancy. (By the way, the ring being a bit stronger, you only need three days of NuvaRing use to be protected against pregnancy). We have worried about causing break through bleeding when you first start pills in the middle of a pack.
Contraception is effective whether you have breakthrough bleeding or not. But all studies reviewed recently in a publication in the May 2013 issue of Contraception showed that there was no difference between break though bleeding or pregnancy rates as long as there was not a follicle that was over 10 mm. So follow your gyno's instructions as to when to start your birth control pills, but she may advise quick start for you.And if that is not quick enough, perhaps another method is best for you. Some methods will protect you from pregnancy the day you begin them. At Women's Health Practice we have contraceptive research trials enrolling, as well as many other contraceptive alternatives.