Same way it has traditionally been done, by setting up puppet governments under their control, going back thousands of years by conquering empires. More recently by the Russians with the Soviet Empire. Japan set up a puppet government in Korea which was a territory of theirs after the China/Japan war of 1894-1895, and Japan controlled it just fine until losing WWII. Japan set up a puppet government in Manchukuo (Manchuria) within China in WWII. Japan did have enough people, they have like a third of our population. Similar to Russia, having few people but held the Soviet Empire together just fine.
The thing about Korea was that it was a limited war due to politics; Americans weren't allowed to do what was necessary to fight off the Chinese. One of the reasons MacArthur lost his job was that Truman wanted it to be a limited war and un-winnable; it had nothing to do with the Chinese ability or inability to fight.
The Red Chinese took appalling losses (in the first winter more died from the cold than combat) and they never showed signs of slowing down; the Manchukuo government could be set up only because the area was the traditional homeland of the Manchus, the last dynasty, that could be used against the republic.
We don’t have enough people to conquer Afghanistan TODAY; what was Japan going to do in China 70 years ago?