Gymnastics is not just about flexibility. Strength and technique are two major factors. I started gymnastics when I was 4. I'm 14 now and at level 9 - it took me TEN years to get to this level, even though I am naturally flexible. Not to mention that to be an elite gymnast you have to, at least, be a level 10 gymnast and win several regional competitions - before you're even considered for the national team. Most gymnasts are "discovered" by national coaches when they are aged 12 - 15. Anything after that is highly unlikely.
Also, gymnastics includes a lot more than cartwheels and back bends. Cartwheels are just the beginning - we have aerial cartwheels on the balance beam. That is a skill that all elite gymnasts can do confidently. Don't forget the tumbling - do you really think your sister can learn to fly in the air, somersault twice, do a double twist, land perfectly, in 3 years?
However, it's never too late to begin gymnastics. Tell your sister to forget about making the national team. Tell her to concentrate, instead, on the actual training on gymnastics. Gymnastics as a recreational sport is just as rewarding as a profession, I tell you.
It's not impossible. But most gymnasts know the saying "If you're not great by eight." When I was 11 I was in level 3, that was January 2010. Now being 14 and in level 6. She may say that 3 years is enough but it's hypothetically not. My guess maybe level 4 in a few years.
She could do collegiate Gymnastics. That is what most gymnasts want. A scholarship. But the national team? It could happen if you have insane talent. But most likely she won't.
Well, let me tell you something, in my opinion, if she does gymnastic forever, it's better for her. She will get better at it, and might be the best at it. So she should do gymnastic forever until she is very old like 60-70 years old, and then she have the right to stop gymnastic, because she got old.
She will have a better time if she stops daydreaming and starts practicing 10 hours a day.
It's probably not impossible, hypothetically, but will take a lot of natural talent and extremely hard work.
Good luck to her.
Of course, just making all-state will be a great accomplishment too.
My younger sister has a question! She is 10 years old about to turn 11 in 2 months and she wants to start gymnastics but still want to be on the national team! She says 3 years is enough do you think that 3 years is enough to become to elite! she is not flexible at all can't do a split or a cartwheel or back bend do you think 3 years is enough!