Were I heading a program (which, disclaimer, I haven't in about 10 years), I think the main things I'd look for are strength, shapes, and above all, understanding how to keep a rigid body.
As far as specifics go, here's what I'd probably want to test them on:
1) Arch/hollow rockers with a coach rocking them by their feet, rather than them making it rock. In other words, they hit a rigid hollow or arch shape, I push their feet up and down, and their job is to just hold the exact same shape, zero change, while I rock them. Bonus points if I can stop them at any point in the rock and they can hold it there solidly. I would consider this the top priority; other items on the list are negotiable, but if they can't do this they're not ready for team).
2) Handstand forward roll. Handstand doesn't need to hold, per se, but I do need to see it briefly stop at vertical with the straightest shape possible, correct head position, and I need to see the forward roll pass through a clear candlestick shape.
3) Backward roll to push-up shape. Straight arms would be nice, but not absolutely necessary; what is absolutely necessary is that once they start extending, they hit that hollow shape and then don't change.
4) Cartwheel on a line. Late turn in the entry, squared up finish, correct hand placement, travel as long as possible, good form
5) Spotted back hip circles on bars with zero change in body shape. The idea here is that they just hold a rigid hollow while I spin them around the bar
6) Straight jumps on trampoline. Can they take off with good form and keep tight form in the air?
7) Sprinting and punching. They don't have to do both in one go, but they should at least understand how to run, how to hurdle, and how to punch a springboard. At this level, I don't much care what happens after board contact, but they should at least understand the components. (I am once again going to be the old man yelling at clouds here: it astonishes me how, more and more every year, so many kids just flat out do not know how to run. They don't spend enough time playing outside anymore, and this is the result)
If they have these basic components, it's super-easy to then develop the necessary skills. If they have skills without strong underlying basics, it's a much bigger headache to go back and try to fix those components.