My pleasure to help. Rather than the checkout, you control your shipping through the Shipping Settings in Shopify. These allow you to choose what zones or regions you'd like to sell to, and also determine what they say.
Oberlo can not import shipping settings for you, because it changes depending on where it is shipping to. You will need to set them up manually, but this is significantly easier if you're only selling to the US. First, here is the guide to setting up your shipping settings. You'll be able to set them to free using this method, and it also explains a little more how it all works.
Second, when you're following the guide you'll come to a part where you can name your shipping settings. When importing products from your US suppliers, make note of the shipping times listed. You can then add those shipping times into the title of the shipping option for your customer. Unfortunately, it won't be for each product, but if they are all coming from US suppliers and being sold to the US, they should be the same.
Hope that helps add some insight!