Most elite gymnasts started when they were between 2-3, but not all of them.
All gymnasts are extremely flexible and very strong. Gymnasts could easily pass the physical tests of the Navy SEALs.
Also, to correct the other information, Nastia Liukin is not tall. No female gymnasts are tall - they just look that way or get talked about that way. Tall for gymnastics is over 5 feet, and the tallest elite gymnast is Svetlana Khorkina at 5' 5".
So short, strong, flexible, and an early start are all good things to have, as well as mental discipline and a bit of a love for risk-taking.