Shipping times are a huge worry for newcomers into the dropshipping world.
I reassure you, they aren't a huge deal.
On your website, have a Shipping Policy page that states that delivery can take 30+ days.
Your goal with dropshipping isn't return customers. It's a proof of concept (in my opinion at least).
Once you're making money using the AliExpress supplier with long shipping times, look into getting inventory and US fulfillment. This doesn't only mean faster shipping times, but branded products and higher margins as well. Plus, fast shipping times/branded products = return customers!
Also, when using Ali, make sure to use E-Packet as your shipping method!