Shipping with Alibaba sellers

I am not sure if this post applies here but because I am an Amazon seller, I am asking here.

Hello,

I am planning to get corrugated boxes for my product. I have reached out to multiple sellers on Alibaba and the sample shipping makes the prices too high. I want to get samples from a couple of sellers so I might end up paying $800-$1200 in sample shipping.
This worries me with the prospect of bulk shipping in the future, I might end up paying more and my product cost will become high.

How do you negotiate with sellers for sample pricing?
Also for bulk shipping what would be the cheapest route I should be taking?

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Thanks in advance.