Given that we don’t know how many people are sick today, it’s hard to work back and figure out how many people must have been sick at any given period in the past.
The article that I read didn’t indicate whether any of the people had come back from abroad or knew anyone from abroad. Whether it was community spread or not would be a pretty significant determinant on whether we’re talking mid-January for patient-0 or earlier.
That said, I would expect that it’s easier for a disease to cross the country than to come from Europe. Despite that, the East Coast brand seems to have mostly come from Europe, at last report, telling us that the West Coast locked down early enough to not impact the East Coast (roughly the end of February, start of March, through corporate recommendations to work from home, previous to the government policies being put into place).
If you’re doubling every 2.5 days, you go:
Day 0: 1
Day 5: 4
Day 10: 16
Day 15: 64
Day 20: 256
Day 25: 2048
If 3 people died in the first few days of February, though, it implies that ~300 people (if we assume a 1% fatality rate) were infected around 11-12 days earlier (e.g. Jan 22). And that would, further, imply that patient zero showed up about 21 days earlier (Jan 1).
That would match what we would expect - that someone came back to the US from China after visiting relatives over the holidays.
However, it seems difficult to have > 2048 people sick at the end of January and not pass the illness off to the East Coast, somehow.
But we definitively now know that there were deaths at the start of February, so I think the safer assumption is that the West Coast did start to spread things by February, out into the rest of the country. However, someone from Europe came in to New York by mid-January and that version simply outcompeted the Western bug.