Absolutely! Simply test for antibodies in everyone who complained of a cold or more severe symptoms from October on........
They did a test like this in Russia a couple of days ago -- random people not supposed to be exposed to the virus at all. 5% had antibodies. What this means is not clear, but perhaps that the virus was all over the world for months, but did not go exponential for whatever reasons.
Russian sample was small (~300 tests), and of course errors are possible... but most likely not.
We do know that the virus was around Washington state for at least two months.. but there is no exponential growth of cases there still. And it did not go exponential in Japan... which is generally a very crowded place. Why?