Interesting, I'd always thought McCellan's best move would be to attack Lee Longstreet's 3 divisions while Jackson's 6 were still at Harpers Ferry.
Essentially the problem with that is the timing. McClellan's troops who were at the front of the column (at South Mountain) had marched all night and then fought all day (Lee pulled back at sunset) and Lee managed to make some distance overnight - it's much safer to march
away from an enemy overnight than
towards them, and Cox's corps seems to have been simply too tired to pursue vigourously. By the time Sykes and Richardson reached the Antietam on the 15th, Lee was the other side of it and fortifying.
With the distance from South Mountain to Antietam being a full day's march, and half of McClellan's vanguard (6th Corps) heading south to try and pin McLaws and Anderson between him and Harpers Ferry (stymied by the surrender), McClellan ended up with his first two divisions reaching Antietam Creek late on the 15th.
The build up by both sides goes:
Confederate
on the 15th: "Evans" division, DR Jones and DH Hill in place
by the 16th: Jackson, Ewell, and Walker arrive
by the 17th: Remainder of Jackson's column straggle in, plus McLaws and RH Anderson
During the 17th AP Hill arrives, plus more stragglers
Union:
On the 15th: Sykes and Richardson (2 divs) form line. Note that Sykes is an unusually small division.
On the 16th: The majority of McClellan's army arrives during the day, specifically 1st Corps, 2nd Corps and 12th Corps come "up" and 9th Corps is coming into position (12th and 9th would be able to arrive by nightfall if they were fed straight in, but any kind of finesse would take more time). This made seven divisions (Sykes is from 5th Corps) at noon with five (12th Corps has only two divisions) more arriving, but there were still five divisions nowhere near the battlefield.
On the 17th: 1st, 2nd, 12th and 9th are available, plus Sykes, and Morell and 6th Corps march in during the battle.
The question is really at what time an attack is considered plausible. On the 15th there's only two divisions actually present for McClellan, and arguably here Lee has the numerical advantage!
Fighting in the morning of the 16th is a bad idea, there's fog and most of McClellan's army was still marching to the field.
By noon on the 16th (when the fog burned off) the majority of Lee's army was closed up, with:
DH Hill
DR Jones
Hood/Evans
Jackson (straggled)
Ewell
Stuart
and Walker having collected stragglers crosses the Potomac at noon. Using the official strength for Jackson when he paraded on arrival, and assuming no return of Jackson's stragglers with Walker, this means that for an afternoon battle Lee has about 25,000 infantry effectives available to him (including Walker) and all of Stuart's cavalry, plus about 186 guns.
At noon McClellan had (in effectives, same as the above)
1st Corps: 8,600 infantry and 46 guns around the Pry House to the Pry (upper) Bridge
Richardson's division and Sykes' division: ca. 6,700 infantry and 30 guns at the Porter (middle) bridge
Artillery Reserve: ca. 42 guns, all the guns that engaged historically
Cavalry: ca. 2,500 and 22 guns
Sedgewick and French (the remainder of 2nd Corps) were at Keedysville, and could fight in the afternoon as they're close. This was about another 11,000 infantry and 30 guns (though Carman's numbers here are perhaps an overestimate).
12th Corps (ca. 7,200 infantry and 22 guns) was at Boonsboro, several miles away, and would only be able to come into action during the evening.
And 9th Corps (11,700 infantry and 32 guns, though again Carman's numbers here are a bit high) were about the same distance from the field as 12th.
This means that McClellan has the troops for an equal battle in the afternoon (about 10% more infantry, half the cavalry and slightly fewer guns) with an extra 19,000 to arrive by nightfall, though again this assumes 9th and 2nd Corps didn't straggle as much as the other Union formations. With Lee on the defensive it's a dangerous risk in the afternoon and a moderately risky attack in the evening, especially as the only way to get 9th Corps into action is to shove them across a bridge right at the enemy. (12th Corps can perhaps come into action in the evening by going across the Pry bridge that's controlled by 1st Corps, though they're unlikely to have time to do much.)
Using campaign strength instead (PFD no straggling) McClellan has 1/3 of 5th Corps, all of 1st Corps and all of 2nd Corps to hand, with 9th and 12th en route.
1st Corps 14,856
2nd Corps 18,813
One division of 5th Corps 6,450
Cavalry Division 4,320
44,439 Campaign Strength
9th Corps 13,819
12th Corps 10,126
23,945 Campaign Strength en route
while Lee has everyone except McLaws, Anderson and AP Hill, for about 50,000 campaign strength. (Via Thorpe: )
This all suggests that an attack on the 16th before 9th and 12th corps had arrived would be a bad idea, because it's an attack against an enemy positioned for defence at equal odds.