The ability of the Americans to deploy atomic bombs was just a few months away from the surrender of Germany in May 1945. With the Germans potentially continuing to fight into the summer of 1945, it begs the question of whether they would have become a feasible target for the dropping of atomic bombs.
(Disclaimer: I am not an expert in Military History. Most of what I know about World War II is from reading about the War in the Pacific and the Wartime Political History of the countries involved. If I get anything egregiously wrong, please feel free to call me out on it.)
I don't know enough about Sledgehammer to answer this exact question, but as something I've thought a lot about before, I'd like to explore a bit about the effects of Atomic Strikes on Germany. For the sake of this scenario, let's say the US (somehow) moves faster on the Bomb and has 2 ready to deploy in November of 1944, 10 months before they did in OTL.
For reference, this is what the front looked like at the start of November 1944.
(The Map is from "Atlas of the World Battle Fronts in Semimonthly Phases to August 15th 1945: Supplement to The Biennial report of The Chief of Staff of the United States Army July 1, 1943 to June 30 1945 To the Secretary of War..")
With the German Air Force not really a significant fighting force at this point the Western Allies probably could have gotten a bomber through to most German cities not east of the Oder–Neisse line. I, personally, do not think they would target any city that was occupied (Ie. Not part of Germany in 1933), and given the amount of bombing already done to most of Germany at this point, there aren't many Military targets left. I think the most likely target would be Berlin, given it's where most of the Government was located, and it could result in a decapitation strike if they strike when the leadership is mostly in the city at the time. The other 2 are Nuremberg and Munich, given that both that enlarged parts of the Nazi political movement before taking power and would be a largely symbolic blow to Nazism as a whole. For the sake of this hypothetical, I'll say the US decided to strike Berlin and Nuremberg.
The effects of such an attack would be huge; assuming the US strikes in the Government center of the city and when Allied Intelligence would have known most of Nazi leadership was in Berlin, the strike would be absolutely devastating for the German Government. Hitler, Ribbentrop, Himmler, Goring, Goebbels, Speer, Dontiz, and numerous generals, ministers, and other lower-ranking Government workers could be killed, entirely destroying any leadership in the country as well. German Armed Forces would probably collapse without any centralized structure for orders and a general confusion about why nobody in Berlin is responding, and with German forces already being stretched thin by late 1944. It is possible that large parts of the military would begin to surrender on the Western Front to Allied forces in the aftermath, as the Allies advance into Germany proper and the Russians take advantage of the disorganization between German units. It is also possible that a Government Minister is still alive, either from not being in Berlin or surviving the blast by sheer chance, and manages to agree to unconditional surrender rather quickly. More likely than not, though, it's pure chaos, and by the time anyone representing the German Government can agree to surrender, the Allies and the Soviet Union have liberated most of Europe and ended the war in effect before 1944 concludes. With the Germans out of the War, it's probable that the Soviets would invade Manchuria far earlier then IOTL, probably around March of 1945, this, combined with the Allies refocusing on Japan, probably leads to the Japanese putting up the flag in May or June, this would take slightly longer then TL without the bombs from what I read, but they would still probably surrender before any land invasion. The main effects of this would probably be merely that all of Korea comes under Soviet Influence.
I don't think the carving up of Europe by the Allies would change much here, except that I think the Allies would be willing to give up all of Berlin to the Soviet Union, there is a lot less of reason to keep it here, this avoids a lot of incidents like the Berlin Airlift and the Berlin Wall, and numerous incidents between NATO and the Warsaw Pact in Berlin during the Cold War, how this effects the Cold War is something that is hard to speculate. I think the largest impact is that in the West, the reception to the bombings are going to be very different then they were to Japan. Japan was an Asian country of Asian people that most of the US and European population had little attachment too. Germany is not the same, many in the US are descended from Germans, Berlin was a well known major city filled with White German people whom many Americans descended from, same with Europe, these are also Europeans that are wiped away in Atomic Hellfire with two cities now largely destroyed as a result. Famous buildings we still have around would be destroyed, cultural artifacts lost, a lot of Nazi leadership would be dead and not face trial, and Berlin would very likely not be the seat of any East Germany Government, with a much longer and more extensive repairs being needed. Not to mention the images of Germans suffering from radiation sickness that would pour out of both cities would leave a far bigger scar in the public, and create more outrage at these weapons being used then was the case IOTL. The war ending sooner also reduces deaths from the Holocaust by proxy, although I don't know of any numbers of how many were killed between November of 44 and May of 45 so I can't say an exact amount of how many, but it is undoubtably a significant amount, including Anne Frank, given that she died in Feburary or March of 1945. I also can't say for sure if that effects the impact of her journal being released, and if it still is, how much it changes it's general impact in history, culture and literature at large. Germany would also undoubtably have lasting cultural impacts from the bombings like Japan did IOTL.
Speaking of which, Japan not being hit by Nuclear Weapons fundamentally changes society in Post-War Japan, the butterflies of this are massive and unpredictable, so I won't speculate on most of them. I will, however, mention that this very likely eliminates the
Gojira character and series, and given the sheer cultural impact of that city and a lot of the rather revolutionary practical visual effects it brought (along with suitmation into the mainstream) this probably creates a massive butterfly on film and media in general, in both the West and Japan in ways I could not possibly predict or even have an inkling of.
In general, the butterflies of this scenario and fucking massive and very hard to predict the aftermath of, especially if it happens in the event of an early D-Day as you've asked, even with a minimal change scenario like this they're massive! I have more thoughts on this scenario, as said I've thought about it a lot in my time (who knows, maybe I'll make it into a full timeline at some point), but this post is long enough as is, so I'll leave it at that for now.