Any overthrow of Hitler in a TL where the Nazis accomplished their main ideological objective of defeating and occupying the USSR making them a true continental power able to fight the UK and America with their full strength is highly unlikely (atomic bomb or no).DOWNFALL would have resulted in 250,000 American dead at least. There is a good chance the Berlin regime would quit just as the Japanese did once they realized the "rain of ruin"; as Truman put, it was a certainty and their "conquests" (Russians are coming or in the Germans' case the Wallies) were no longer viable. The Germans were not THAT STUPID. Even a Himmler or a Goebbels cannot stop their underlings from killing them and suing for peace on any terms that allows for a chance of personal survival. (As Hirohito personally did through his ministers, I might sarcastically add.)
The July 20th plot aside (which only involved a few hundred members and came about because the war was going badly for the Reich and the plotters thought they could make peace with the WAllies and continue fighting the USSR), the German military leadership never broke their oath to Hitler and attempted to overthrow him. IOTL almost 800,000 German troops died between June and August 1944 and the German government/Party leadership didn’t throw in the towel. In the last 5 months of the war in Europe over 1.2 million German troops died along with hundreds of thousands of civilians and the surrender only occurred after Hitler was dead and Dönitz was named his successor.
First generation atomic bombs (10 to 20 kilotons) aren’t war winners or miracle weapons like modern nuclear weapons. They’re just bigger bombs that require only one plane instead of 1000. They wouldn’t be as effective against German cities as they were against Japan due to the difference in construction. IOTL Hitler, the Nazi leadership and the High Command weren’t fazed by the numerous fire bombings and destruction of German cities (to the point where the WAllies were running out of targets and had to attack smaller and smaller targets), millions of citizens killed, starving, sick or made homeless, millions of enemy troops on German soil and the use of hundreds of thousands of conscripted civilians (including the elderly and children) as cannon fodder.
Why would an atomic bomb somehow have the required impact to make a coup happen against the men who restored the Reich to greatness, vanquished the Jewish Bolshevisk menace and conquered the highly sought after Lebensraum when all of the above factors mentioned didn’t (hand waving the difficulty of actually dropping an atomic bomb on a German target)?
There was ample opportunity (especially in 1945) for the High Command and the government to overthrow Hitler and surrender in the face of the Allied onslaught but yet it never happened whether due to their oaths to the Fuhrer, fanaticism, fear of reprisal for them and their families if the coup failed, fear of Allied prosecution, love of country, military professionality, responsibility for atrocities, etc.
If a coup didn’t happen IOTL when Germany was almost entirely occupied and on the verge of defeat why would it happen when they now have control of most of Europe from the English Channel to Russia along with increased resources and military power with the only major combat theater being North Africa?