Without nuclear weapons the US would not be able to defeat the Nazis and their European Allies on their own.
The Americans and the British never fought the main body of the German Army until 1944. By that time they had command of the air, a secure and well stocked supply base in Britain and a German Army pinned down and bled dry on the Russian Front and starved of fuel. Even then it took the W Allies (combined) 11 months from Normandy to the Elbe when 2/3 of German troops were facing the Russians.
A USA fighting alone would have to replace British, French and Canadian troops and logisitics, supply all their own air cover, provide all their own ships and then take on 200+ German and Axis divisions that could be brought against them. I don't see things ending well for the Americans.
Even with nuclear weapons the USA on her own cannot defeat Germany, as she also would need some means to deliver the payload to the target, with reasonable changes of succes, which is a challance on its own, given the huge distances needed to cover. (Trans Atlantic returnflight and quite a large distance into a continent as well, not even discussing possible defences en route.) Also expect German retalliation against the USA, which could mean counterattack with newly deveopped long range "Amerika Bomber" type aircraft, which had been on the drawingboards since the early 30's, but tactically not proceded with, as all conflictzones were on German borders so far, not requireing extreme intercontinental aircraft. With the war in Europe over, the project was likely to be revived and with German industry fully intact, likely to bear fruits. Also noticable, the USAAF had zero experience in air defence over their own ground, as never in history the USA mainland had been threatened by aircraft. Germany had this experience and developped defences for this purpose.
In theory, a USAAF nuclear attack would at its soonest take place around 1945, some three years after the collapse of the USSR, as mentioned by others. By that time the Germans would have had some means themselves to retalliate in one way or another, possibly with their own weapon of mass destruction. This would certainly cause concern in the USA, as never in history had the mainland been threatened and their own intelligence wqould be aware of this, causing the government to back down seriously from suicidal attacks for no purpose at all. If the US Leadership was stupid, which is unlikely, a nuclear strike might occur, possibly not at Berlin as this target was too far away in well defended territory, but at a target nearer the coastline, such as Bremen, or Hamburg, or even in occupied France, or Russia. The retalliation would likely follow soon, as memtnioed above, causing severe casualties among civillians in the USA, most likely in the New York and Washington DC area. As mentioned the USAAF had no experience in homeland defence and both New York adn Washington DC are near the East coast of the USA, making a direct attack possible form across the Atlantic. (In 1944 some prototype German OTL aircraft flew a few miles out of the coast of New York in testflights of ultimate range aircraft. If such a thing in the OTL, with massive bombing of German Industry,was possible, one might think what would have been possible with a German Industry intact.)