*** Moved from Bringing Family of LPR forum to Moving to the US & Your New Life In America forum, where similar topics about processes after US entry are discussed ***
1. If your wife selected the option in her DS-260 form to receive SSN, then her SSN card should arrive in the mail within 2 weeks or so of her US entry. If it doesn't arrive in 1 month, she should book an appointment at the local SSA office to apply for SSN in person.
2. The moment CBP stamped her F2A visa, she already became an LPR, authorized to work. No need for EAD. Her F2A visa + CBP entry stamp serves as her temporary green card for 1 year, equivalent to the plastic GC for any legal purpose, including employment and travel.
Have you paid the $220 immigrant fee for the plastic GC?