(TEB) Teterboro Airport is the most important and widely used private aviation airport in the United States for private aviation, and the #1 business jet airport in NYC.
For international travel, Teterboro Airport offer customs in two locations: Hangar #1 and the Jet Aviation FBO. Although the airport is open 24/7, customs hours at KTEB are between 7:30 AM – 11:30 PM local time, however, special accommodations may be possible upon request.
After clearing customs, we can arrange for private helicopter rentals for quick transfers to the East 34th Street Heliport, the West 30th Street Heliport, or the Downtown Manhattan Wall Street Heliport. Luxury ground transportation is also available.
Epstien had to land at an airport where he could clear customs which is why the customs aspect is important. Customs agents will sometimes come to the plane (inspection). He could have been stamped on the plane before arrest.
Just speculating...