No, the supplier does *not* handle it if you are shipping by sea. At the sea port, it is your responsibility to set up a local courier service for them to pick it up and send it to whatever address. It’s more complicated than this, but you can also just do door-to-door courier service for direct shipping.
In your situation I would look into finding a forwarder to handle all of this for you. A good freight forwarder will handle the transportation of your goods from the suppliers factory to Amazon’s warehouse, including customs, import duty, etc. It makes your life a lot easier when you don’t have to worry about all of that stuff yourself.
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