The Allied plan in the Pacific was was to ruinously firebomb Japanese cities, have the Soviets enter into the war, and then to invade the home islands (Operation Downfall). The atomic bombs were not brought into this plan until relatively late, when it was determined for sure that they would work. The use of the bombs was both as part of a hope that they might hasten the end of the war to avoid US invasion (though this was not scheduled until November 1945, so the timing was not so tight as people sometimes get the impression), but also to potentially pre-emptive the Soviet invasion (because the US by that point was no longer thinking that having Soviet influence over there was a good idea).

So I would suggest that you are posing the question the right way. It was not the case that the Allies planned their operations around the idea that the Japanese would surrender after the atomic bombing (and Soviet invasion). In fact, the Allies were caught a little off-guard when the Japanese did surrender as quick as they did and it required a lot of work to shift their gears from an invasion plan to an occupation plan. The Allies had no assurances and certainly no confidence that the atomic bombs would end the war.

Michael Gordin's Five Days in August is all about this period of uncertainty between the first use of the bomb and the surprising discovery that it "worked." (It should be noted that whether the atomic bombs caused the surrender or whether the Soviet declaration of did is a matter of historical dispute.)

It is also worth noting that they would have almost certainly used more atomic bombs had the war continued into late August 1945 and beyond.