Lincoln fired on Fort Sumpter? /s
Close enough. He sent the warships with orders to fire on the Confederates. The only reason the confederates fired on Sumter was because the first of those ships had arrived, and according to their orders, the ships would soon be attacking the confederates around Sumter.
The confederates would not have attacked Sumter without the arrival of those warships with their belligerent orders. It was the sending of those ships that caused the war, and the members of Lincolns cabinet had told him that would be exactly what would happen if he sent those warships.
They were correct.
Ergo, Lincoln did in fact start the war.