ESTA applications may be submitted at any time prior to travel. The processing of an ESTA can take up to 72 hours.
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.
A passport is an internationally recognized travel document that verifies the identity and nationality of the bearer. Only the U.S. Department of State and U.S. Embassies and Consulates have the authority to grant, issue or verify U.S. passports.
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.