Well this is incorrect. Assuming you are referring to the "Star of the West", that ship was not unarmed. It was loaded with Union troops intending to be sneaked into Fort Sumter. It was also carrying munitions.
President Buchanan initially wanted to send the Brooklyn loaded with troops to Sumter, but then he thought this would provoke a war, so he ordered the USS Brooklyn to offload the troops onto the Star of the West and sneak them into the fort secretly.
As the troops were being transferred from the Brooklyn, (out at sea where they thought they wouldn't be seen) southern ships nearby spotted them being moved and they immediately sailed to shore where they telegraphed the Confederate authorities that the Union was attempting to sneak troops into the fort disguised as a "supply" mission.
This alerted the people guarding the harbor that the Star of the West was a belligerent ship intent on moving soldiers and munitions into Sumter, and so they fired at it.
Bet you didn't know these details. They don't teach stuff that makes the North look bad.
That’s why the fleet was sent and the South attacked the fort before it could be relieved by the fleet IIRC.
If one ship (Star of the West) could suffice to resupply fort Sumter, then why would it be necessary to send 5 warships, and an ocean going passenger ship loaded with soldiers and munitions? (the Baltic)
Here is an image of one of your "supply" ships.
It is clearly an 1860s era warship, and it wasn't even the most powerful one they sent.