The atomic bomb dropped on Hiroshima (Little Boy) was a U-235 gun-type mechanism. There was no doubt it would work. The bomb dropped on Nagasaki (Fat Man) was a plutonium-239 bomb (almost twice as powerful as the U-235 bomb). That bomb worked by using Pu-239 compressed by conventional explosives to reach criticality and release energy (implosion type bomb). The trinity test conducted in the desert of New Mexico on July 16, 1945 was of that type to ensure it would work. The U-235 gun-type bomb needed no final test to ensure that it would work.

See: The Making of the Atomic Bomb by Richard Rhodes for excellent detail and explanations of the entire Manhattan Project.

Yes there came a point in the project when the scientists were sure that the U-235 bomb would work. At what point did they reach the conclusion that such a bomb could be built? If they were so sure, why weren't all the combatants racing to make one? And on what date did the Soviets conclude that the west would eventually have a working bomb and what did they think would be the date by when the west would have it?

The complete design for the U-235 bomb was completed in Feb., 1945; the components still needed constructing and the main problem, then as now, for those wishing to make the simple type atomic bomb, is the arduous cost and time in processing enough natural Uranium to get the needed mass and purity of enriched U-235 for use. The U-235 bomb (Little Boy) was not assembled until July, 1945. That was after the separate components had been manufactured, tested, and the proper amount of enriched U-235 available.

The Trinity Test conducted July 16, 1945 proved 100% the viability of the Pu-239 bomb (the scientists were certain the U-235 bomb would work; but politicians need absolute certainty, thus the Trinity Test proved 100% one bomb would work ). I assume the knowledge of the successful test was known to Truman at or just before the Potsdam conference, which started on July 17, 1945 and lasted until August 2.

Others (including Germany) were pursing atomic weapons, the theory was known to all – the reason the American’s came in first is an interesting, convoluted, and remarkable story that I will not detail. See the book I referenced. Suffice to say that certain things worked in America’s favor and the sabotage of Germany’s heavy water facility in Norway by allied commandos (mainly Norwegian resistance but also allied bombing) was a stroke of fortune and genius. The reactor was knocked out of service by early 1943. This was a major blow to critical material and experiments required for atomic bomb construction. The Germans never recovered from that blow.

Truman learned of Trinity at the conference. Stalin probably did too, before Truman told him.

The question was, was there an actual nuclear deterrent to Russia taking on the west in May 1945. The US had no bomb until July and the Russians probably knew they had no bomb in May.

The German nuclear program was a low-priority academic-only project that had been effectively shelved because an evaluation concluded that nuclear fission had little practical military applicability. The sabotage of the Norwegian heavy water facility made the allies breath easier, but it did nothing to prevent the Germans from getting the bomb, because the actual German program could not have produced a bomb for many years. The Russians winning the ground war is what kept the Germans from getting the bomb.

If the bolded part is the main question then No, "the west" did not have the actually bombs needed to be a deterrent to "Russia taking on the west in May, 1945." And in fact could probably not have produced enough bombs in a short time frame to be truly effective even after August, 1945, except in a shock and awe manner. In August, 1945 Fat Man and Little Boy were the only atomic bombs the US had at that time. I think the estimate on producing additional atomic bombs would be on the order of weeks at least, to two months. They could produce the Pu-239 bombs faster than the U-235 bombs (much faster to produced the needed amount of Pu-239 in a nuclear reactor).

I disagree somewhat with the last paragraph but it is minor. I would add that the German's themselves (as you alluded to) made the biggest mistake in regard to pursing Atomic weaponry. Time, material, available scientists, and energy were diverted to other concerns thought more pressing. In that context the Russian ground war probably played a factor. But I'm not that versed in this aspect of WWII so must defer to those with better knowledge.

Communist world - no
More dangerous world as more closer to the edge of the beginning of a new war - yes

I think it's funny that anyone could be so confident of "curb stomping" the USSR. If history teaches us anything is stay the **** out of Russia. During WW2 the Soviet upper command was perplexed at why their motorized units kept running out of fuel. It's because the troops were drinking the gasoline. I think it's safe to say that it's a bad idea to try to fight people like that.

people interested in this should check out a really good new book:

Command and Control: Nuclear Weapons, the Damascus Incident, and the Illusion of Safety by Eric Schlosser