General Gustav P.T. Beauregard started the Civil War when he fired on Fort Sumter in Charleston Harbor, South Carolina.
Lincoln recognized Fort Sumter as the most visible Federal fort in the newly formed Confederate States. He ordered a relief force to bring supplies to the fort.
President Jefferson Davis of the Confederate States decided it would be better to attack the fort before the relief party arrived.
Davis could have postponed hostilities had he not attacked the fort. He could have tried diplomacy: demanding that all United States military personnel leave the Confederate States. Or, demanding that the United States turn over possession of its property in the Confederate States. It probably wouldn't have happened, but at least it would have turned the beginning of hostilities back to Lincoln.
Lincoln did not want to be the attacker. He needed those in the northern Confederate States, such as Virginia, and were not as bitter as, say, South Carolina, to continue to support the Union.