One way of doing it is:-
Make an appointment in advance with the local FSDO and go there when you arrive in the US. They will check all your paperwork and issue you with a Temporary Airmans Certificate.
Then you go do your Flight Review and the instructor will endorse your logbook to confirm that you have done it. They write an entry like:
"I certify that blah, private pilot, certificate number pending, has satisfactorily completed a flight review of section 61.56(a) on (blah date)."
You're legal to self-fly from that point on.