Planning Your Trip. The travel document usually arrives within 150 days (sometimes longer) after submitting your application. You can't leave the country until you have your approved travel document in hand, so you should expect to spend the 3–5 months after submitting your green card application in the United States.
If you are a permanent or conditional permanent resident who has been outside the U.S. for one year or longer, apply for a re-entry permit before you travel. Use Form I-131 - Application for Travel Document. For permanent residents, the re-entry permit is valid for two years from the date of issue.
(U) When USCIS or ICE authorizes Advance Parole, they issue an I-512 or I-512L form, Authorization of Parole of an Alien into the United States, directly to the individual applying for Advance Parole. This will allow the traveler to request parole from CBP at a POE when they return to the United States.
ESTA is an automated system that determines the eligibility of visitors to travel to the United States under the Visa Waiver Program (VWP). Authorization via ESTA does not determine whether a traveler is admissible to the United States.