No. One needs a valid passport to travel internationally. A birth certificate is no substitute and ads nothing.
A consent letter is recommended for all cross-border travel, even for a day trip, if the child will be travelling alone, with only one parent, with friends or relatives or with a youth group.
The US government places no restrictions or requirements on you when exiting or entering the country with your child. Many foreign governments might require require documentation for entry or international air carriers to board their plane.
Ing to USCIS data from 2023, the average processing time for Form I-131 (Application for Travel Document) varies between 3 to 7 months, depending on the service center handling the case and the specific category (e.g., refugee travel document, re-entry permit).
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.
Applications may be submitted at any time prior to travel to the United States. The Department of Homeland Security recommends that travel authorization applications be submitted at least 72 hours prior to travel.
No. You cannot file a Form I-131 to obtain a reentry permit unless you are physically present in the United States when you file the form.
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.