It takes several weeks for the FAA to process an aircraft registration application. For up to 90 days during this processing window, the aircraft is legal to fly but only within the United States under what is known as a temporary authority. If you need to fly outside the US during this time, you will need to file a declaration of international operations. This can be done in person or by fax. The FAA will process it on an expedited basis, often within one day, and issue a temporary registration, allowing international operations for 30 days. Of course, before those 30 days are over, you should be issued your permanent registration, making international operations permissible.