You can open bank account without SIN. I bank with TD and till date they don't have my SIN. Now usually for new immigrants, most banks issue credit card when you open checking account so that you can start building your credit history. So for that, yes, you need SIN. But if you are willing to let that go, they would let you open account without SIN.
Outside of bank, for POA, I would recommend applying for DL(Canada allows DL exchange if you are from certain countries) or photo card that acts as id. You don't need to show POA for applying. Until the physical card gets mailed, they will issue you a temp ID that can also be used as POA.