@hafer -
That's an awesome diagram, what did you use to make it?
Also,
I've played this like 6 times now and I can get to the brink of (but not quite take) Minks on my first turn on normal.
Haven't completed the turn yet but all the air and the bulk of the ground fighting is done. Now I just have to pull up HQ's and air and secure a supply corridor. I probably wasted some of my INF finishing off the last Russians when they really should have headed east. Those units were doomed anyway and you don't get a bonus for early kills!
My units on the gates of Minsk hammered away at that one stack of Russian units but it only seemed to make them stronger! They will head east next turn while the second wave of armor finishes Minsk off.
The key it seems is to use your slower inf to open up a gaping hole in the enemy lines so your faster armor and mech don't have to waste even a single AP to get to their target. They just roll through the open terrain while the rest catch up from behind. That seems to be the only way to reach the back objectives in 3 turns. Of course, against a stiffer front line, they would have to participate in the breakthrough itself, but not here.