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 TPS beneficiary applying for a new travel authorization document, you should continue to use Form I-131, Application for Travel Document. If you have a pending Form I-131, you do not need to file a new application.
If you are requesting expedited processing of a travel document, you generally need to apply for and obtain the document before you leave the United States. You should make your expedite request on your pending application at least 45 days before you plan to leave the United States.
To apply for TPS travel authorization or advance parole, you must file Form I-131, Application for Travel Document. If you are filing Form I-131 together with Form I-821, send your forms to the address listed for your country.