Yes, my experience has been that there IS a minimum age for application. I tried to help register my daughter in the IACRA online registration tool one day before her 14th birthday two years ago and it would no accept her application because she was one day shy of being 14 years old.

I had to register her early on the morning of the Big Day, then drive her to the DPE 30 miles away to get her paper Student Pilot certificate so that she could then solo that afternoon.

You do not need any license to start training. You do need a license to fly solo.

It would appear things are getting harder, not easier, especially for our young people. And according to this Federal Register wording FAA is still considering measures to make things even more difficult for all pilots in the future as photos and other new biometric measures are still on the table as far as they are concerned.

The one hand giveth, and the other hand taketh... and the giveth getteth shorter.