You can look into your own home insurance company, the one you already had or some other to see what they can provide. Usually they would insure you for some time when you arrive but then you would have to change status when you start working there and actually living there, not just as a tourist.
You can also see with your bank and a bank in general as they also provide some health insurance services sometimes that could be an ideal transition period for you before getting a proper via your work or a specialised health-care company.
Again be aware that health costs a lot in Hong Kong along the line of the USA so make sure you know what you are doing.