How about India? They will soon be the most populated country in the world? Indonesia has about 250m people? Brazil, Pakistan, and Nigeria? All these countries have large populations. They probably have a lot of "growing room" too.
In short, this claim is meaningless:
"China has 3 times the population of the US. As soon as they started growing a middle class, it was inevitable that this would happen."
That gets into the societal aspects - after working for their basic subsistence, how much time in the day is left for working on other things that they could sell. In the US, the creation of industrial-scale farming meant that food became plentiful and cheap enough so that there was capacity & time left over for work that could then be used to create a profit.
There are other factors at play of course. India has an enormous bureaucracy that soaks up much of their excess capacity and stifles innovation. The remains of the caste system also means that some of their most productive people aren't working effectively. Nigeria is doing much better these days, but still suffers with a large amount of corruption. Pakistan & Brazil - I don't know enough to comment - perhaps you can fill in why they aren't growing as fast as they might.
In short, this claim is meaningless:
"China has 3 times the population of the US. As soon as they started growing a middle class, it was inevitable that this would happen."