Well here you start competing at age 8 in year, our 'pre-team' is for gymnasts aged between 5 and 7. Usually at 6 1/2 - 7 they enter our squad, but it depends on physical and mental maturity and skill level.
There are 2 head coaches at my gym - myself and one other. We are both in charge of our women's artistic squad and I am in charge of the pre-team also. One of our pre-team's training sessions is the same time as our beginners rec group - and the other coach and I are both in attendance. We both begin spotting talent on day one - looking for things like posture, good listening, who can make corrections, who has good balance, agility and co-ordination etc. As the weeks go by, we start looking at how fast a learner they are, strength, flexibility etc. We usually send letters for a trial out after they have completed 1 term. The trial is held over a 3 month period, so that we can get a really good idea of whether the gymnast enjoys it, and if they are right for the squad/the squad is right for them.
I must say that I'd like to be slightly more picky! However, we also take into consideration gymnasts who approach us and ask whether they could be part of the pre-team - If they have the desire to learn, who knows, they may end up better than a gymnast who is super talented but has no desire!