Greetings, and welcome to ParrotForums!! I understand you very well!!
That you can clip wings after one week surely means he is very tame!! Your bird seems in very good feather. This is often a problem with cockatoos as they may pluck feathers when unhappy and/or fed an unhealthy diet.
Unfortunately it is very difficult to judge the age of a parrot once they mature. Perhaps a skilled vet can determine age within a few decades, but even that may be a guess.
Scott is very correct!!

not like any of us doubted....
Most birds you can only tell the very young and the very old. One of the few exceptions is a Scarlet macaw who actually get 'wrinkles' on their face

But even then, its a guess for 'decades' such as Victoria's evil new friend Red is somewhere between 30 and 40 best guess due to his face.
But, for most birds, even bloodwork is not always an answer. For example, my bare eye too when she first came home was not quite 3 years old, but her blood showed very early stages of liver disease, not something a vet would ever expect in what appeared to be a perfect healthy example of a bare eye too. Then on the flip side, you have a bird like Victoria's Kelly who at 33 years old having lived on a crappy seed diet, in a home with multiple smokers and in a way too small cage with one dowel perch, had bloodwork of a young perfectly healthy bird. So, go figure that one!
If you can, take your beautiful new baby in to a good avian vet, have bloodwork done to make sure he/she is healthy and then get her onto a very healthy diet with lots of fresh veggies, and love her whether she's 2 or 20
Side note, if she is only 2 years old, in 3 years or so, you'll definitely know she was very young when she hits sexual maturity

If I were you, I'd hope for her to be 10, 15 or 20 and well past that often problematic stage!
Best of luck!!