Plenty old enough to shoot, and then some. Cougars IME retain juvenile spots and bars inside the legs, especially inside the front legs, up to another year or two after they leave their mother. The spots/bars get fainter all the time, fading out slowly.
I have seen young adult, independent cougars that were operating solo that still have faint spots and bars inside the legs. Technically, according to the WA State Game Regs. it is apparently illegal to kill such a cougar, though it is virtually impossible to see the faint spots in a calling situation. Weird law given how long cougars retain juvenile spots.
Anyway, the cat in the photo above has no trace of juvenile spots/bars inside its legs that I can see. It's a grown up.