This POD is tricky enough in itself - even if McDowell wins at Bull Run and the green Confederate army breaks and runs all the way back to Richmond (doable, I suppose) Union armies still have the whole western half of the South to conquer and military leadership (Frémont, Halleck, McClellan) and doctrine (trying to take cities as opposed to eliminate armies) that are going to severely handicap that.
But let's pretend that Richmond / Davis / the Cabinet are all taken by surprise and the leaderless CSA comes apart at the seams in under a year. What happens?
Lincoln makes some progress on slavery, but not a lot. The issue isn't that he "didn't much care", because checking the expansion of slavery was literally the raison d'être of the Republican Party, but in 1861 there simply isn't the political will for full-scale emancipation, especially in a world where the Confederates surrendered rather conditionally and their armies were essentially unharmed - and Dred Scott makes most solutions short of a constitutional amendment unfeasible. So Lincoln probably does what Southerners were afraid of pre-war, which is appoint minor Republican office-holders in the South and Republican Supreme Court justices.
We also *maybe* get constitutional amendments banning secession and protecting slavery where-it-currently-exists and nowhere else, although on the latter I dunno if Lincoln has the negotiating position to actually get a South that is being readmitted in under a year to agree to that. From there you get a (very) slow growth of the Republican Party in the South via patronage which, with the Southern fear that Republicans wanted the slaves to rise up and kill them all, is not exactly going to be calm and violence-free.
The Republicans get more and more frustrated at a Democratic minority that can stifle much of their legislative agenda in the Senate and is literally willing to murder southern Republicans, while a new generation of existentially-threatened white Southerners start telling themselves that if Davis and Granny Lee hadn't been such cowards they could have fought a "real" war.
And then they do fight a real war.