The U.S. did not reinforce Pickens until April 12th, when orders to bombard Sumter had been given and after attempts to force the Union forces out of their fort. It was Davis who resorted to war.
".......To embark with Captain Fox, you will cause a detachment of recruits, say about 200, to be immediately organized at Fort Columbus, with competent number of officers, arms, ammunition, and subsistence, with other necessaries needed for the augmented garrison at Fort Sumter" April 4
Naw, we cain’t take Lincoln at his word here:
"You will fit out the Powhatan without delay. Lieutenant Porter will receive Captain Mercer in command of her. She is bound on secret service; and you will under no circumstances communicate to the Navy Department the fact that she is fitting out." BTW, That's April 1