Inbound shipping for Inventory is not posted to COGS; it isn't sold, yet. If the shipping is on the same charge listing as the products, you simply allocate it into the products, the same as any sales tax you paid. You enter it into QB not the same as how it is listed on the receipt to you.
If the shipping is a different provider, you post that to Other Asset. Then, you use Adjust Inventory, and allocate the cost per item name, for inventory to be fully costed. Like this example:
I have a client that handles sporting goods. We get Shipping, pallet fees and broker fees Not from the manufacturer. That means we use "other charge" items that all post to Other Asset. Then, we list the actual products on a Bill for vendor name = WIP; we list everything that we got, as items, fully costed from the total in WIP. We click on the Expenses tab and remove that value from the WIP account using a negative. Hit Recalc= this is a $0 Bill and considered paid.
Now the products are on hand fully costed.
WIP = work in process.