The US Strategic Bombing Survey, conducted in 1946, concluded that:

Based on a detailed investigation of all the facts, and supported by the testimony of the surviving Japanese leaders involved, it is the Survey's opinion that certainly prior to 31 December 1945, and in all probability prior to 1 November 1945, Japan would have surrendered even if the atomic bombs had not been dropped, even if Russia had not entered the war, and even if no invasion had been planned or contemplated.

There are other present-day sources which conclude the same thing, based on projections for Japanese food supplies (they were indeed quite isolated at that point due to blockade) and knowledge about the internal workings of Japan's high command.

If the surrender terms had been modified (e.g. from "unconditional surrender") it becomes almost a sure thing. If the Allies had given assurances about the postwar role of the Emperor it would have given those in the Japanese high command who favored a "diplomatic" solution a significant edge.

It is even today not clear that the atomic bombs were what caused the Japanese surrender; there is strong evidence that the invasion of Manchuria by the USSR is what precipitated the surrender in August 1945.

Anyway, there is obviously no way to know, but there is a rich literature on this question. Tsuyoshi Hasegawa's Racing the Enemy is a good place to start, as he lays out the scenarios very well. Anybody who tells you the alternatives were "drop two atomic bombs on cities in rapid succession without warning" versus "an invasion that kills millions of Americans" is trying to pull a historical "fast one" on you. The reality is a more nuanced and complex.

I think Russia was always planning to invade, and wished to control the Northern Island after the war. The Allies had different objectives regarding Japan. US wanted to finish the war as soon as possible but Russia wanted to conquer areas under Japanese control. So encircling, however feasable, probably would not have happened.

At some point the Japanese might have had to surrender, but even if they didn't, they would no longer have been a threat to the world, compeltely trapped to their islands and with no materials coming in.

In a lot of ways that is what the Navy leadership favored. Nimitz with King's backing favored continual blockade and bombardment of the islands as opposed to invasion, through the Spring and Summer of 1945. And when the plans were essentially postponed to see what the bombs would do, King didn't necessarily consider the invasions going forward a foregone conclusion, but had to put up a united front for the new President.

And the Pacific Fleet under Nimitz did all they could to make life miserable in the islands, the inland and Japanese seas were patrolled and mined by subs, carrier planes strafed and bombed almost at will, and even the battleships and cruisers moved in to shell coastal targets.

But also consider the feelings of the public in Summer 1945. Germany was defeated, and more than anything growing sentiment was to end the conflict and bring the troops home.

To have to maintain a blockade without a fixed end would have meant keeping additional millions of men overseas, with all the attendant risks of loss of life. While we can point to some contemporary estimates and post war analysis, the fact remains that if the US and allies had committed to simply starving Japan out it would still have required huge numbers of men and ships and planes without a definite end date.