Lincoln was not about to accept the southern rebellion, but to say that he had given up all hopes of a peaceful solution and had decided on war is, I believe, false. Davis needed the war more than Lincoln did, and his actions showed it.
Why didn't Lincoln just let South Carolina have Ft. Sumter? Why draw a line at Sumter when you allowed the Confederates to take over other US installations throughout the South?
You don't let them have the fort because you are going to force their hand... and the South was a willing and complicit partner to having their hand forced.
If his intent was NOT to start a war then why send warships instead of a resupply vessel? Why plow ahead with the warships after being explicitly warned by half your cabinet that doing so would provoke war? Why refuse to meet with negotiators who had sought to resolve the thing peacefully? Why send a letter after the war was started there informing the commander of the expedition that its outcome --meaning war-- was the desired effect even if the expedition did not go as planned?