My oldest has mild ADHD so we put her in gymnastics as a physical outlet. My second one was also doing flips on the couch so naturally we found her the safer option. My youngest wanted to do what her big sisters were doing!
My daughter is a high energy thing and spent most of the many, many months of UK lockdowns from 4-5 bouncing on our sofa and trying to do handstands. I promised to get her into a gymnastics class when the gyms reopened. Had her booked to start Jan 2021 then we had another lockdown so she didn't get to start until May 2021.
She immediately adored it and never stopped trying to learn handstands and cartwheels - within a couple of months her coach asked her to come to a second recreational class, and a couple of months later moved her to his WAG foundation squad group where she's been thriving ever since and making great friendships. She is always upside down.
Her little brother picked up a recreational class a couple of months ago because he fancied it - he loves it but I think he'll stick to rec because he has none of the crazy drive/compulsion his sister does. He just enjoys the hour he's there - his passion is reserved for piano!
I put my oldest kid into a rec program when they were about six, and the youngest was not quite three. I asked if it was possible to put her into the class as well--I think the age cutoff was 3 or 4, I don't remember. The coach was wary but said she could try a couple classes.
The older kid never did figure out how to do the basic skills and quickly moved on to other things (athletics is not their thing at all). The youngest took one look at all the trophies on the wall and made getting one of those her goal. She's been breathing gymnastics ever since.