Not gunna happen.
I coach our competitive League Club at the High School in the district I work for and we have a strict no one under 16 rule because of the regulations for tournament enrollment and transportation issues.
From what I can tell the percentage of 13yr olds who can actually manage to show up to practice, take it semi seriously, and then perform under pressure is incredibly low these days.
The first year we did it we let anyone attend and 16+ could compete, but it was a total mess. The second year I only allowed 15 people total to join and everyone was 16+ and we did well and did not have any of the constant emotional and personal issues as the year before.
I don't think you will be seeing any organized competitive league for those under 13 on anything other than a case by case local level.