Correct me on my dates, but was'nt the North Africa campaign wrapping up in May or April '43? These units would'nt have time to go right back into battle at Normandy. The US would be using green troops for the invasion.

I have to dis-agree on the air superiority not being a factor. In mid '44, the Allies had hammered the German infrastructure. Also German armor could not move during the day time with Allied air ruleing the sky. They would not have this luxury in '43. The Germans had far more pilots and gas than in '44.
Again, correct me on this date. But was'nt the P-51 with the Merlin just starting to be mass produced in mid '43?
Rommel, just getting back from North Africa, would'nt have much time to strengthen his defences in Normandy in '43. The Allies might have gotten ashore easier but I don't think their dash across France would be. This timeline here puts the western allies ahead of Russia by a year. Would the Yalta agreement have still been? Germany feared Soviet occupation more than British or American.

<I also think that they could have pushed across France by early 1944 and been on the Rhine nearly a year earlier than they were originally.>quote.
Even if they did, were they prepared to take Berlin by themselves?

Eh, just some of my thoughts.