Maybe not.
After dropping Little Boy and Fat Man on Japan the US would not have enough Special Nuclear Material for a bomb for at least another year.
We would have won in Europe in 1945 and have had to continue to fight Japan perhaps for a year or more after.
I am aware that in 1945 we had a strictly limited number of Bombs. However, if they were our only effective method of destroying Germany it is possible additional resources would have been pitched in earlier and we could have had more by 1945. Or possibly what they produced was all that was possible.
Or we sit in UK for a year and then nuke the crap out of Hitler with our next batch of a couple dozen Bombs. It’s not like he’s got anywhere he can hide.
A more interesting scenario is whether UK would have fallen without an Eastern Front to divert the vast majority of Hitler’s forces.
In 1944 the Western Allies faced 1.5M to 2M Germans and allies. The Red Army was dealing with about 4M. How do you think things would have worked out for US/UK had they faced another 3M Germans in France and Italy?
The numerous factors involved make it difficult to compare numbers, but in general the western allies had to deal with about half the number of Germans that the Reds did.
In 44/45 we had about 5M men on the western front, facing about 1.5M Germans. And we still had a difficult time.