Ming from Agents of Speech explains how to teach non-verbal children to imitate words, starting with vowels and building up. She stresses that skipping imitation training can mask the real problem: some kids have physical barriers to speech, others just don't understand imitation yet.
When you go from a simple vowel, it's much easier to go up to a word level and therefore you need to take a step by step approach. That's why when you're thinking about getting your child from non verbal to verbal, there are loads of different reasons why your child isn't able to do it. One of the reasons is because there might be some structural problems or neurological problems that actually prevent your child from using speech imitating speech. But if you're talking about a child who doesn't understand the concept of imitation, then all this would work as well. And by the way, if you don't do all of this, all the action imitation, the learning to learn skills, first, you will never know why a child is non verbal because you haven't even gotten to a level where you can test the imitation. A lot of the diagnosis or speech disorders can only be done when imitating when verbal imitation is established. Other than that, it's all guesses. It's very difficult for a therapist to give you a concrete answer about what's going on.
