Can my wife start collecting SS at 62 based upon her own benefit and then later take the higher spousal benefit when I apply for SS at FRA - about 3 years later?
Potentially, yes, but she'll keep the reduction that she took on her own account for filing early.
For example, say your wife's full retirement age benefit rate (PIA) is $800, and yours is $2000. If she files on her own record at age 62, her benefit amount would be reduced to around $600. Assuming that she was born after January 1 1954, she would then be deemed to apply for an excess spousal benefit when you file for your benefits, and the unreduced amount would be $200, or 50% of your PIA minus her own PIA. That unreduced rate would also be reduced if she is under full retirement age when you file, and if she is 65 when you file, the reduced amount would be around $183. That excess would then be added to her reduced retirement benefit, giving her a total benefit rate of $783 (i.e. $600 + $183) in this example.
You may want to consider running the maximization software available on this website before making any filing decisions.