Xiao long bao (soup dumplings) moved from a regional specialty to a recognized American food in stages, and the timing is a little fuzzy because there was no single launch moment.
The first big push came in the 1990s, mainly in New York and Los Angeles. Shanghai-style restaurants in Manhattan's Chinatown and in Flushing, Queens, served them to a growing mix of diners, and food writers began singling them out. Joe's Shanghai on Pell Street is the name most often linked to that early reputation.
The next wave came in the 2000s, when Taiwanese chain Din Tai Fung opened its first U.S. location in Arcadia, California, around 2008. Its popularity and the long lines that followed pushed xiao long bao into mainstream American food coverage.
I'm working from memory on these dates, so please treat the exact years as approximate. If you want firm dates, look for restaurant reviews from the period in the New York Times or Los Angeles Times archives, and for the company's own history on Din Tai Fung's site. Anyone who remembers when they first saw soup dumplings on a U.S. menu, feel free to add it.
@FieldNotes, one date to fix, since you flagged the years as approximate: Din Tai Fung's first U.S. restaurant opened in Arcadia, California, in 2000, not 2008. Wikipedia's Din Tai Fung article gives 2000 and says the founders' son Frank ran it directly rather than as a franchise. So the Los Angeles side of the story starts about eight years earlier than the reply above suggests.
The New York side matches your 1990s dating. Per Wikipedia on Joe's Shanghai, the original opened in Flushing, Queens, in 1995, with Manhattan Chinatown and Midtown branches following. It calls the pork-and-crab xiaolongbao the restaurant's most famous dish and notes a two-star New York Times review by Ruth Reichl in 1996. I couldn't confirm an opening year for the Pell Street branch itself, so I'd treat any exact year for it as unverified.
A rough picture, then: Flushing in the mid-1990s, Los Angeles' San Gabriel Valley by 2000, and the wider national wave after that. I couldn't verify when the dumplings first reached U.S. menus before that, so I'd love a first-hand memory. Who remembers their first soup dumpling here, and where was it?

