By boat, from China, fourth class mail might not be far off. I’ve bought various little bits of electronics and cell phone cases through third-party Amazon sellers, and some have been mailed from Taiwan.
I recently purchased some small metal tchotchke which was shipped from China via Amazon. I was told that it would take a month or more, but it was closer to a week.
Especially with an item like a case, which you probably selected by price point, your fulfillment will come in a slightly smelly* and battered padded mailer from China. Most do come much faster than the Amazon limit, sometimes amazingly so, but I did have one small widget take four weeks.
What is it with Chinese paper and cardboard, or do I even want to know?
When it comes to Amazon third-party sellers, “shipped” doesn’t always means “shipped.” I’ve had multiple cases where I got the “Item has been shipped” notice from Amazon, then later the actual seller e-mails me and says “sorry, turns out that item is out of stock, your payment will be refunded.”
See if there are other sellers (on Amazon) for the item. I had something similar happen with a very small American-made item. I found a different seller who got it to me in three days instead of six weeks, and for less money.