Normally you're supposed to be able to sort out most things and get a SSN in big ports of entry. But with the COVID-19 I'm not sure if this is still possible to register for SSN.
The PR cards will be sent by mail to a Canadian address that you need to provide upon entry. I heard it normally takes around 8 weeks for the cards to be sent. You can ask someone to receive the cards on your behalf and send them back to you in the US because you will need the PR cards to reenter. Otherwise you can pay a private PO box at UPS or something like that (needs to be a private PO box) that will forward mail to you in the US.
I read that only 4 airports currently operate intercontinental flights (Vancouver, Calgary, Toronto and Montreal) but they may reopen other routes this summer. You'll have to check that.
PR card processing is now taking 200+ days since processing has stopped. If you mailing address is clearly a PO box your application can be refused processing.