Yes. You have to gather all the evidence thats needed (Doc's letter, Letter from your employer in case of business trip, etc) and take an Infopass appointment. At that point of time, you will be given an appointment to meet with an Immigration officer at the local office, where you can present your case. They will approve and provide you with a temporary AP using which you can travel. Carefully track the validity period etc and make your travel plans.
If you are still on H1 and have a valid Visa and an 797 Approval for extension, you could still travel, but I am sure you might have considered and ruled out that option, maybe.