My kids have been in AWANA a number of years. But currently my 2nd grader is not involved for various reasons (that aren’t worth listing here). I found a “Memory Work Notebook” from Great Commission Publications to be a nice supplement.
It lists memory verses and catechism questions at the beginning level for a 3 year old. The child then progresses through each level. They have it listed for 3 year old through high school. If you started your child when they were three, this would not last through high school. But I think that this book can be used by students in high school as they are foundational verses to the Christian faith. So I am assuming that is why they have the ages listed the way they do.
Here is something I have only seen a quick glimpse of, but it seems very similar.