Help with a young student's setup

I've been teaching for a few years, but only students who are nine and older. I've generally had good success with my students and they have played well as long as they practice.

Today I had a six year old girl come in for the first lesson. I have a lot of ideas for how to tweak things for my next lesson, but one thing I am stuck on is her setup. The shoulder rest she had didn't seem to be working for her and I couldn't get the violin positioned quite right. She was not able to hold up the violin without using her hand. I swapped out the shoulder rest with an appropriately sized sponge shoulder rest I had on hand, but it had the same problem.

Trying to be more specific here: the shoulder rest made contact with her shoulder, but the sides of it did not. I felt that the support needed to be closer to her maybe, so perhaps the sponge would solve that. However, with the sponge, her head was positioned too far forward/drooping and I had a lot of difficulty adjusting it more to the side.

I have not had a similar issue with my older students.

What troubleshooting ideas can I try? What are possible reasons for this? I feel like a grossly disqualified teacher (but I know there's a bit of a learning curve for teaching younger students too!)