We have established suppliers now, many of which we originally found through Alibaba/Aliexpress, and we order hundreds or thousands of items at a time (I run a small chain of cell phone repair shops), but even then shipping on a couple medium-sized boxes can run $80 and up.
Most sellers on there only have China warehouses, and the free shipping option is 2-4 weeks+.
You can check whatever you're interested in on AliExpress though. It's the consumer version of AliBaba, which means the price and shipping info are always included in the listing. AliBaba is the one where you need to negotiate all the terms: Price, shipping, minimum order quantity, etc.
The absolute best (when the vendor has ePacket, which is like the FedEx of China) is 7-12 days.
But even then, you need to expect 2-5 days for the vendor to actually package and ship the item.
So you're much better off quoting customers 3-4 weeks. If 1-3 days is all that works for your niche, you probably need a new product, unfortunately.
Is it because all products are coming from the far east?
I'm looking into making a dropshipping app, but for my niche anything more than 1-3 days would be a non-starter.