It is well documented (and explained in horrific detail in the book Flyboys) that the broiling and burning of Japanese by dropping incendiary bombs caused a tremendous amount more structural damage and loss of life than both atomic bombs combined.
So were the atomic bombs inevitably necessary to end World War II? Not really. The war would’ve ended eventually, either with total (or near total) Japanese destruction or a unconditional surrender. Did the atomic bombs speed the decision to the unconditional surrender? Some would argue yes. I would argue no, however.
As stated earlier, the fire bombs dropped on Tokyo and numerous other cities in Japan caused far greater damage than the atomic bombs. The atomic bombs were simply too expensive to produce and far riskier to drop than several hundred B-29s ready to pour liquid fire on the people (err, targets) below.
The fire bombing was the greater threat to the Japanese at the time, not the atomic bombs being dropped.