Can you explain what you mean by "commercial quantities"? I ask because early on, in the late 1800s, Chinese were already able to get a lot of specialty ingredients. Things like cuttlefish, bamboo shoots and the like. Basically since the beginning of any sort of large-scale presence of Chinese in the US.

As the population grew, and especially after the Chinese Exclusion Acts were repealed, the availability of foods kept up. The Chinese communities in the US have pretty much always had access to Chinese food, at least once the first group of migrants was established.

But if we're talking like H-Mart level stuff, then that's going to be a different answer.