She most likely has no chance of being on the national team regardless of anything within your control. But that doesn't mean anything. A more realistic goal or decision making metric would be to make it to a level where she could do NCAA gymnastics. It's relevant that the current gym does not seem to be training anywhere near close to this level though.
Making the national team (which would generally happen within the next five years) would require the circumstances to line up perfectly. It's not just ability. You need the right coach, right facility, right body type, avoid injuries at crucial times, be willing to sacrifice, right personality, not fearful. So that's why I say don't base all your decisions on that because it is not all within your control. You may find there are no gyms in your area that train at the elite level. But you would have a much better chance of finding a gym with recent NCAA gymnasts, which is still an EXTREMELY challenging level of gymnastics that 99% will never reach.
As far as TOPs, if she could naturally do the strength moves, there might be a chance. I have coached one child who could have done well in physical abilities six months after starting, and caught up to her age group in skills the next couple of years. But TOPs tests are summer so depending on when her birthday falls there probably wouldn't be enough time to be ready. That doesn't mean she couldn't ever catch up as a 12 or 13 year old, just that within a year or two it might not be realistic.
The first thing to do would be to try a gym that has level 9 and 10.