The Americans wanted to invade Northern France as early as 1942, and were only dissuaded by British arguments of unreadiness (mainly put forward by Britain's chief of staff Alan Brooke). After Tunisia, or possibly even towards its end, the Americans wanted to invade Northern France, and were only dissuaded by British arguments of unreadiness. After this, American patience with British unwillingness to invade Northern France was running out. Summer 1944 was about as late as the Allies could invade Northern France without the US going it alone. There was always a suspicion among the Americans that they were being used to fight a British war for British interests.
The Dieppe raid put paid to the notion that a successful invasion could be mounted at that time.
Lack of air cover was crucial and the technology to get the troops off the beach was not there. The tanks never made it off the beach.
The raid was a complete failure, despite the heroism of the troops who included Canadian units as Calgary Red will know better than me, and yet when Rommel took over command of the Atlantic Wall he assessed it as inadequate to resist invasion and immediately began to strengthen its defences.
When one looks at the things that made DDay successful, it is hard to see how a successful invasion could have been achieved prior to 1944.
The Tunisia landings and the invasions of Sicily and later Italy, were a testing ground for tactics and technology.
The Salerno landings were rescued by naval bombardment by battleships, yet even then a lack of air superiority allowed German glider bombs to put Warspite out of action.
This lesson was learnt and D Day saw total air superiority as a prerequisite, in tandem with a massive bombardment by naval forces.
Mulberry and PLUTO were essential to the success. Without the supplies and especially the fuel, the invasion would have stalled within sight of the beaches.
The real chance the Wehrmacht had in preventing the success of DDay was stopping the invasion on the beaches. The airborne assaults on Pegasus bridge and the Orne canal, and the causeways behind Omaha beach were designed to delay the German responses, and the intelligence war which planted the idea that the the real assault was at the Pas De Calais, all enabled the allies to get a secure beachhead.
Hitler dithered and Rommel was prevented from throwing his panzers at the beach head by a fractured command line.
In short, a practical invasion of Nothern France was not feasible until it happened.
As an aside ... What I never understood, was the fact that Stalin wanted US and U.K. material support and we shipped arms and materiel to Archangel that originated in the US, with appalling loss of life and ships.
To me the safer more efficient route was via the West Coast and Siberia.
Edit
Here is the Wiki link to the Dieppe Raid
https://en.wikipedia.org/wiki/Dieppe_Raid