The trouble is, the Trust system was specifically set up with ShB in mind and it's dungeons were designed especially for Trusts in that the dungeons' mechanics were programmed to allow for the more limited Trust AI, and further, it was because the story no longer could get away with using other players to help you (as in 'other Adventurers', as there is no Adventurer System in the First), so the Archons were used instead to fill in. Before that point though, the story assumed you were gathering a party of fellow adventurers to help you, hence no need for Trusts. The Grand Company Squadron are hence made up of generic 'adventurers' with no real personality or backstory.

Unfortunately, due to issues with dungeons' mechanics shown with the Squadron, it seems that SE will not be able to retroactively add the Trust system to pre-ShB dungeons and trials I'm afraid.