Can a person be too young to have an addiction problem?

No. One can be born with an addiction problem, depending on the mother's choices during pregnancy.
No. Addiction is the body's physical need for a chemical/substance. This need has been seen in newborns and even the fetus in the mother's womb. This addiction problem, however, is the "physical" addiction, not the "psychological" addiction. To develop a psychologic addiction, one must have greater brain function; the "want" vs. The "need.".
Yes. The brain in its young years has more neuroplasticity therefore easily altered. Chemical dependency starting at a young age also is commonly associated with factors such as bipolar disorder, genetics ie alcohol and opioids , sexual abuse depression all contribute greatly to the disease of addiction.