Why are the trinessa birth control pills colored differently for different weeks. I began taking it?

No it was not as mistake you start with the white pills.

Oral Contraception
To achieve maximum contraceptive effectiveness, TriNessa must be taken exactly as directed and at intervals not exceeding 24 hours. TriNessa is available in a blister card with a tablet dispenser which is preset for a Sunday Start. Day 1 Start is also provided.

Sunday Start
When taking TriNessa the first white tablet should be taken on the first Sunday after menstruation begins. If period begins on Sunday, the first tablet should be taken that day. Take one active tablet daily for 21 days followed by one green tablet daily for 7 days. After 28 tablets have been taken, a new course is started the next day (Sunday).

For the first cycle of a Sunday Start regimen, another method of contraception should be used until after the first 7 consecutive days of administration.

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Day 1 Start
The dosage of TriNessa for the initial cycle of therapy is one active tablet administered daily from the 1st day through the 21st day of the menstrual cycle, counting the first day of menstrual flow as "Day 1" followed by one green tablet daily for 7 days. Tablets are taken without interruption for 28 days. After 28 tablets have been taken, a new course is started the next day.

If you have started this way then contraception is effective immediately.

The tablets are different colours because each colour contains a slightly different amount of hormones. Make sure you take the tablets in the correct order.
If you are still unsure talk to your doctor or pharmacist.