Congratulations on your job offer. Yes, in most cases you will get your SSN within 2-3 weeks. The green card takes a month or so. SOmetimes they call you for additional biometrics, which could delay your GC a bit. But, as
@nervouswreck said, you can still use your I551 stamp in your passport in lieu of your green card for up to one year, so that should not be a problem. Some employers may allow you to start working as long as you would produce the SSN within a specific time period. If you explain it to them, they may agree to let you start work, and only get paid when your SSN comes in; this has been done before.
Good luck.