Yes. They just need to have an adult on the account with them, usually mom or dad, but it can be a grandparent, aunt, uncle, or other adult. This kind of account is called a custodial account. The kid or teen (referred to as the minor or beneficiary) owns the stock, while the adult (the custodian) has legal responsibility over the account.
Once the minor is of age, the assets in the custodial account legally belong to her. We can help her open an individual account and transfer the assets from the custodial account into the new individual account.
What will she do next? We think she will be thanking you profusely for having had the foresight to open a custodial account and invest in her future!