The only reliable way is to have access to the phone. Verizon, appropriately, has protections to prevent anyone from getting access to your texts. It makes no separation based on age or being a child.
Since there is multiple ways to text and message, there is no single way to see all the texts. There is no way without having the child's phone get alerted that someone is getting messages. There is no way without knowing all the app passwords and appleid password.
You can look at message plus from Verizon, but that will only show SMS text messages and not iMessages. The child's phone will still get notification and need to approve the monitoring.