Can you get the Bangladeshi consular officials to update your passport with an amendment/endorsement about your full name or even issue a new passport with your name as it appears on your US permanent residency card? [Bangladeshi consular officials do it for women based on marriage rather easily; but for you as a male, I don’t know if they would be as amenable to doing so since it wouldn’t be a maiden name-related change.] If you can get the Bangladeshi consular officials to do that, that will remedy most any potential problems for such situation and be a longer lasting solution.

If you cannot get an amended passport or new passport from Bangladeshi consular officials with the initials spelled out instead with those two first names in full and get it done in a timely manner, you should still be ok with the docs in hand if all other biodata elements across the documents are an exact match; but there is no guarantee that the airline or a non-US border control official won’t make an issue of it.