Not necessarily; the first few carriers don't seem to have successfully seeded outbreaks, in general it takes a few attempts to get a disease like Covid established, and almost all countries seem to have stopped it spreading directly from China including closely-linked ones like Taiwan but also places like the UK and US. As far as I can tell something just went really badly wrong in Italy that no-one is interesting in examining too closely, and when this spread Covid to other countries it was spun as proof the other countries had screwed up and failed.