@robto correctly captures the rapidity of the decisions on Korea on *both* sides, the lack of long and deep prior thought about Korea’s future, and American and Soviet under-valuation of Korea compared to almost ever other location in China or Japan, during WWII, truthfully, until the start of the Korean War.
Thus it also captures some of the randomness of the 38th parallel demarcation.
The hinge of fate could have easily swung either way, to a demarcation line further north or further south. At Potsdam and after, neither the Americans nor Soviets, increasingly wary of each other, valued Korea enough to make a hard line on *that* land a make or break issue in their relations. It only became a sticking point, and symbolic, after the occupations were set up.
Bonesteel and Lincoln thought about requesting a 39th parallel divide [which matched on historic Tsarist proposal to Japan] but trimmed their sails and decided the 38th was adequate.
Had they stuck to the 39th, the Soviets in Potsdam, not wanting to make trouble, and securing their most vital objectives of Japanese islands, a secure border for Vladivostok, and control of Port Arthur all north of that line might have agreed without a fuss! I tend to think that would have been better, at least in the long run, for Koreans, Americans, Japanese and the world.
Conversely, had the Soviets at Potsdam been instructed to put forward a bold proposal, at least initially, for occupying all Korea, or Korea north of the 37th or 36th, the Americans might have felt fairly powerless to do anything besides accept the Soviet proposal on its face.
In reality, the Soviets touched parts of the country long before the Americans, on the Soviet first day of combat. After Japanese surrender the Soviets could move even faster. But so could the Americans have, even though they took several weeks in the event.
So from Japanese surrender August 15th really the whole western and southern coast of Korea and both capitals were still up for grabs if the Soviets and Americans chose to race. The Soviets had the definite lead on the northeast coast. Michael Sandusky argued in his book the Americans could have airlifted and sealifted at least Marines into their zone of Korea and beyond weeks faster than the historic occupation of southern Korea, but that as theater commander, MacArthur dictated and stage-managed a rigid and sequential timetable that ensured Army personnel were flown in to Japan first before other U.S. armed elements, including himself in grand ceremonial style, before any troop and ship movements onto the Asian mainland were permitted.