I think the easiest way for a union victory is a quick crush at Bull Run followed by a march onto Richmond.
Everyone keeps saying Bull Run, but I don't know why; the same reasons the Confederates failed to capitalized on their victory IOTL will be affecting the Federals here, in that they have an extremely Green force that cannot be expected to rapidly move to occupy strategic terrain before the defenders can rally. Manassas is over 100 miles from Richmond, after all.
The Northern army is really only a
third of the size it needs to accomplish this task purely militarily even after Bull Run (and on top of manpower reasons there is the speed and unpreparedness issue), but the psychological effect on a quick victory might encourage many Southern commanders to trade surrenders for pardons. Remember that the Confederacy has questionable legitimacy and losing in the very first stage could very well lead to "we're sorry" instead of a fortification of Richmond.
The only problem is that this might lead to a Northern victory at 1861. I can fix that. We'll call South Carolina full of pigheads who think the Confederacy of Seven is viable without Virginia and North Carolina and SC spends the rest of the war trying to persuade the deep south that while their state militia fights the federals. Logistics and a green army keeps the federals at bay another three months before mop-up operations can start.