That is absolutely not normal!
I'm surprised any coach would be on board with this idea. There is a minimum age requirement for Level 10 for a reason. Injury and burnout are the obvious reasons, but also the fact that proper technique and safe progressions take time. In my opinion, the absolute earliest a kid should be competing Level 10 is at ten years old.
I know of a girl who got to Level 9 by age 8. She was obviously extremely talented, but her gym pushed her too far in terms of difficulty. Her back handsprings on beam were terrifying. She switched gyms about a year later, and the new gym took the time to correct her technique. She reached Level 10 by 11, and is currently competing HOPES. Had she not switched gyms, she would have most likely retired due to the constant injuries she had there.
Another example is a gymnast who reached Level 9 at 9 years old. She was probably the most talented kid I've ever seen, and would have definitely made elite. However, she only did gymnastics because of how much her parents wanted her to be an Olympian. She eventually left the sport when she was 12. She returned to public school and started exploring her own interests.
The reason I'm telling these two stories is because they show that getting to a high level super early is most likely not the best idea in the long run. Most elite gymnasts get to Level 10 at 11-13, so there is no rush.
