I remember reading it was "undocumented" Chinese nationals who were traveling back and forth between China and Italy. One of Italy's largest textile factories is literally within miles of the Wuhan lab and many speculated that many of the workers were moving back and forth and brought the virus from the factory to Italy.

But you are correct in the fact there is no denying Italy was hit very early on, well before many realized what was going on. I remember seeing an article were Italian doctors were concerned they had five deaths in a single weekend from new strain of influenza they hadn't seen before.