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?
He sent both.
Why refuse to meet with negotiators who had sought to resolve the thing peacefully?
Because their demands were unacceptable. The so-called negotiators were there to gain recognition of the legitimacy of the southern rebellion, something Lincoln would not do.