This is very common. The only thing that is needed is to have a good shipping partner on the China side, capable of handling everything. One of the reasons a product should go to a warehouse first is if the goods are shipped in a container with other products, and the cartons need to be split up first so they can go to multiple addresses.
I’ve seen cases where the supplier does everything. Have them label. Set up the shipment in seller central, and have the supplier palletize everything for the multiple destinations Amazon spits out. Keep this shipment open while goods go across the ocean. After freight arrives, request pick-up at the freight forwarder’s DC from Amazon appointed carriers in seller central. You freight forwarder should have experience doing this. This approach moves the labor costs (labeling, de/repalletizing) to the China supplier, where the labor costs are much lower.
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