Hello there,
the card effect of Profundity allows to set aside a small ship (Command 1). It allows so: " Before deploying fleets , ..." If this ship is the flagship the player normally wouldn't deploy his/her flagship during setup.
The second player could have " Surprise Attack " as one of his/her objectives. Objective Card says: " While deploying fleets , the first player must deploy their flagship before deploying any other ships."
Now we discussed what would happen if the first player would choose to play "Surprise Attack".
FAQ states: "Ships and squadrons that are set aside are only affected by the ability or card effect that set them aside . They cannot be deployed by a different card effect than the one that set it aside." ... "A set-aside ship can only be assigned tokens or chosen as an objective ship before being set aside (by Blockade Run or Intel Sweep , for example) those tokens or effects are not removed when the ship is set aside."
A) Objective overrules upgrade : Objectives are chosen before deployment. First player cannot set aside his flagship. He/She must deploy the flagship first.
B) Upgrade overrules objective : The set-aside flagship is not affected by the objective card. The first player deploys another ship first.
C) Autoloss : The set aside ship cannot be deployed. First player cannot legally deploy and looses automatically. (That could easily be avoided though.)
What's your judgement?