One could say that the War commenced with the attack on Mr. Sumner, not with the attack on Fort Sumter.
But one should not, unless one is using the word "war" in a metaphorical sense, as in "war on women", or "war on poverty", "war on belly-fat", etc.
Insurrection, rebellion, domestic violence, lawlessness, vigilantism, etc... sure.
But strictly, war is an action between sovereign states, and is often officially declared as such.
Imho, that's the reason why the Confederacy on May 6, 1861 formally declared war on the United States, or in their own language, "recognized" that war existed.
Formally declaring war is the act of an independent state, intended to distinguish itself from accusations of being mere "rebellion" or "insurrection".
Rebels don't declare war, and neither do states formally declare war on rebellions.
But states do declare war on each other, hence the Confederacy's action of May 6, 1861.
The United States officially treated it all as rebellion, and never formally declared war.