Ft. Sumter was under siege even before the shelling started. They cut off supplies and threatened to stop any resupply. That is itself an act of war. Lincoln’s position was quite clear, he wouldn’t start hostilities but he would do what he had to do to keep all federal installations in the south. The south chose war, and yes the common sentiment was all for it. And the common sentiment in the north was for war if needed to keep the union together. But the south initiated it, and no historical revisionism can change that.
Lincoln's cabinet told him the sending of those warships would start a war. Major Anderson said it would start a war. The person who is responsible for starting a war is Lincoln, and no one else.