That is a very difficult question. For a child to reach any of those goals they need to have the drive and determination to do it as well as a good skill level. A child can start at 2 and have all the best training but never make those goals or a child can start much later than expected and with talent and determination achieve it all. Also the age of starting gym is not as much the key as the age they reach key points in their training.
but if you are looking for averages. Our average gymnast who reaches the highest levels usually starts somewhere between the ages of 4-7. Kids who start at a younger age like 2 don;t usually in the end have that much advantage over a kid who starts at 6. Often 6 year old beginners are put in the same class as 6 year olds who have been doing it from 2 and you don;t always see that much difference in them.
If your goal is college you do have a clear age limit, kids usually go to college at age 18. Recruiting becomes big as age 16 so they will want to be a solid level 10 or an excellent level 9 by 16. This being the case they would want to be an optional gymnast by 13 at the latest. And a level 4 by 10 at the latest unless they are one of those very talented gymnasts who may do multiple levels in 1 year. Most kids don't do this. This being the case there is really no need to start before 6. For college the expectation would be the same for women as for men as the age they start college is the same.
Elite is different. There is no age limit on elite, a gymnasts could become elite at 30 if they wanted, but this is of course rare. It takes many hours of training each week to become elite and most adults don't have this sort of time. Girls can compete as senior internationals in the year they turn 16, ideally they would compete as junior internationals by the year they turn 14. So level 10 by age 12 at the latest would be the goal. Optionals by age 9, level 4 by age 6 is ideal. In this case gymnastics would need to be started by 3 or 4.
Men for elite is different. They must be 18 to compete internationally and their competitive career will last for a lot longer than a women. In the women the athletes shine from 16-22 on average for men being older means more adult muscle and a better advantage (as long as they don't get injured). Men will be limited in what they can do before their bodies go through puberty so rushing through the levels will help them very little. Level 4 is not really needed until about 9, level 7 not really needed until about age 12.
