With the CR1/IR1 visa, you are entitled to start working as soon as you enter the US. You don't need to wait until you get your green card (mine arrived 7 weeks after entry and I began employment after 3)
As for the SSN, mine arrived 2 weeks after entry - I had ticked the box on the form for it to automatically generate one for me. If you didn't, you'll have to go to your local office to get one sorted. I'm not sure about working whilst waiting for one though