I don't think we'll ever know the real answer as to whether the virus originated. In the modern connected world where you can travel between any two points in under 24 hours it's going to be near impossible.
Many of the reports and studies (such as the Italian one) showing very early spread are not definitive, but what is pretty clear now however is that Covid was spreading in Europe (and almost certainly North America) in December. By mid December the UK was facing an influenza pandemic (https://www.independent.co.uk/news/health/flu-deaths-hospital-ill-patient-gps-vaccine-phe-a9244201.html) and a big increase in deaths. Was this really Covid? We'll probably never know.
We do know that the "mystery cough" was present in the UK long before official Covid cases were reported. https://www.bbc.com/news/health-52589449