Yes, you can have unprotected sex on green days: this means that you do not need to use a barrier method (such as a condom) on green days.*
You can trust the first green day you get as long as you see it on the Today view. Please ensure to check your daily fertility status each day before having sex.
The algorithm will only distribute a green day if it has enough data to support that you are not fertile for that day, either by confirming that you have ovulated or unlikely to do so within five days (sperm survival).
You can learn more about red and green days here.
*Keep in mind that the only contraception method that protects against STIs is the male and female condom. Should you have a reason for concern, be sure to use them regardless of fertility status.