I've been saying since Dressrosa that I believe that Green Bull and Fujitora might have been Bounty hunters prior to the WG draft. That would explain how the Marines knew about these two monsters in the first place. If they had been capturing criminals for years, and turning them into the Marines, then they would have already been on the radar of the World Government. Not just for their strength, but to also make sure they don't stray off, and become criminals themselves.