The maze,
I don't know why some of the people here are saying you cannot get a credit card. I have gotten a credit card from TD Bank with no SIN#. You do need a Canadian address to do it however. I decided to do this before I moved over in an attempt to build credit history before I arrived. (I did this in December of 2014 and I moved here July 2015 (SIN# obtained after PR).) My husband called TD Bank and made an appointment in advance that I wanted to open a personal checking account as well as a joint account and requested a credit card (in my name only). The limit on the credit card was very low (either $500 or $1,000, I cannot remember. It was called Green VISA.) Hard to use a card with such a low limit, but I tried to use it as much as I could. By the time I moved here, they said I could get a different VISA card with a higher limit, so I switched over. I now have a card with $5,000 credit limit (which isn't as high as the limit I was used to back in the US, but it's high enough that I could use it without worrying about going over the limit). Someone who moved here told me there was a couple of banks who have new comer packages - One was TD Bank and I think the other one was Scotia Bank (CIBC may have it too.) I believe you can do all this even if you are single. Someone who moved here a while back advised me to open a bank account to get a credit card as soon as I could, and that's exactly what I did. I am keeping one US credit card and US bank account open (You will need a US address for this) - I've been told if I ever decide to go back to the US to live with my husband, I will still have credit history as long as I have a bank account and a credit card. Without them, you will have to start the credit building all over again.
And get the bank statements in paper instead of paperless - I used it to get my healthcard in Ontario (They requested that I gave them proof of residence (I couldn't exchange my US drivers license to the Ontario one so this came handy.)
And oh, try to get Global American Express in the US now - That is supposed to be transferable to Canada. I happened to get a wrong AMEX so I couldn't get that transferred..