In early April various Union units received information of nearby Confederates. This information was usually dismissed by the high command (Grant and Sherman) as simple scouting parties, home guard or pure imagination. Some of these encounters ended in bloodshed and capture. Sherman may have been overcompensating for when he was perceived as insane while in Kentucky because of the warnings he raised as commander there.
It would have been easy for Grant to have ordered a reconnaissance with enough strength in infantry and cavalry to find out what was in front of them. A point made at the presentation was that this area is not good for cavalry operations, the forests are just too thick. On the battlefield this is correct but for scouting operations it might have made the cavalry's job easier. The Union cavalry would have been mainly confined to the roads, but so was the Confederate army. The Confederates would not have been hiding off in the woods and by the afternoon of April 4 there were too many Confederates to hide.
Depending on the day this reconnaissance was made they may have learned very little or a lot about what was in front of them. Maybe the battle would have started earlier, but for the most part it seems safe to assume the Grant's army would have been better prepared for a battle.
The lack of a proper reconnaissance prior to the battle has disastrous consequences at the beginning of the battle. Good information would have probably meant a more prepared Union army. Some of the information Sherman received was good, it was just ignored. This was a critical decision and mistake.