HI Erin,
A group of parents can start up a group without approval from the principal, but it's not the best way to go. If you reach out to the principal and share your ideas on why a PTO would be important for your school community, you may find that you and the principal have more in common than you think.
You want to avoid having an adversarial relationship with the principal if you can.
We have some good articles about working with the principal that you may find helpful:
Hello, I am trying to start a PTO at my school. To make a long story short, my principal is not very supportive but this PTO is greatly needed. So my question is what makes a PTO official and do I have to have my principals blessing on this? How involved does the principal need to be?