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.
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.
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.