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?