not a lawyer but in principle yes, you have to explain the issue to the officer and they let you get in. different story if they approve your green card few days before leaving the US: in this specific case you can't travel, because you have to wait your green card or get a special temperary stamp in your passport which I don't remember the name rn

If the I-485 is approved while you are abroad, your AP may technically no longer be the main entry document because you are now an LPR, but you may not have the physical card yet. If you also have valid H-1B visa/status documents, entry may still be possible, but this is a tricky timing issue. Have someone check your mail; if the card arrives, consider having it securely sent to you, or contact the airline/CBP for boarding options. If you have any other questions, feel free to ask them in our next Lawfully office hours session! - Attorney Rashmi Bishnoi (All information shared here is for general educational purposes only. It does not constitute legal advice or create an attorney - client relationship. Your situation may require fact-specific guidance. For personalized legal advice, please consult an immigration attorney directly.)