To which they should accept "I have just applied for one" and a copy of a work permit or PR card along with the receipt from the application.
You shouldn't be providing a fake SIN number, but the paperwork from Service Canada literally says on it that you can provide proof of application for a SIN to your employer. If your employer is stupid enough not to be able to recognize that some people have to apply for SINs, I can't help you.
Seriously, this isn't that hard and we're scraping our brain cells for no reason. If you can apply for a SIN but haven't, apply before you get an interview. If you get asked for a SIN and haven't applied yet, tell your employer you will apply and send the receipt from the application. Boom.
