Could he have survived without contributions from mankind.
And I am not talking about his support crew.
He got too important contributions that were artifacts of human existence. The first being the trash that washed up on shore. I don't have a problem with him using this, I think he was simulating a shipwreck survivor. Second, the feral goat. These again are really nothing more than junk that washed up on the shore.
3,000 years ago neither the trash nor the goat existed on the island. It appears to have very few natural resources which is why it is uninhabited. There are very small, very remote islands in the Pacific that manage to support human populations.
Other than the goats the only other terrestrial mammals seem to be rats. I imagine he could eat those. Also, there seems to be no basalt rocks which are very beneficial for making stone tools. He was lucky that piece of metal washed ashore to use as a blade.