Yes, permanent residents can get social insurance number on the same day of landing.
As I said before, once your landing is completed at Port of entry. Go to nearest 'service Canada' office. Show your COPR and passport. Sign a form and get SIN number in 15 mins.
If you are landing in Toronto airport, there is a service Canada office in the airport itself.
I am not sure if service Canada office is there in other Canadian airports. It might be inside the city.