To the best of my knowledge, you can not re-arm that BMP.
If you want to add weapons to it, it helps to first remove all the hand grenades and drop them somewhere else or in the ammo crates.
What works best for me is to follow the team to the first objective. Try and be the first one there and eliminate the opposition.
After that objective has been completed and you become the Leader, go back and get the BMP.