Are your back teeth already adult teeth?

Yes, the back teeth are already adult teeth.

A human has two sets of teeth, the deciduous teeth, also called baby teeth or milk teeth, and the permanent teeth, or adult teeth. The permanent teeth begin to come in around the age of 6 and typically replace all the baby teeth by the age of 12 or 13.

The back teeth are among the last teeth to develop and may not fully erupt until a person is in their late teens.