I think it took us about a week to get the initial GE approval. The interview may have to be scheduled within a month of approval, “scheduled” that is “set on a date.” But, there was no available interview slot within a month for us, the earliest available at our airport was 3-month later. So I picked a date 3-months later and then kept checking the website (using automatic tools) and managed to find cancellations within 2-weeks. I think JFK had a plenty of openings within a few days. Certain airports are better than others.
Oh, the GE card shows citizenship so you can carry that as an ID or you could get a passport card.