My lawyer has an option to file the application before step 3 is ready. I'm not a lawyer and did not see the form myself. As I understand, with regular processing first they hold your application in the envelope, then they open the envelope, register your application and continue waiting, before starting any processing. Step 3 is required only when they actually process your application, which not happens for two months or more. So if your lawyer files regular a month before you have the score, you save the first waiting period. Then if you convert to premium, USCIS can process in several day as your application is already registered. But again, consult a competent lawyer.
Thank you for your advice IMrach. Can you explain more regarding the timescale and process for applying for H1B before passing Step 3 or when the results come out? Is there a place on the H1B form that asks for the Step 3 score? Or is passing Step 3 required at the very end just before H1B approval? Thanks!