Brendan here from the Shopify Support team.
Providing estimated delivery dates is possible in your store already if you're using Shopify Shipping through USPS or Canada Post. Rates delivered this way will have an estimated shipping time provided by default to the customer as shown here.
Alternately, there are apps that can deliver this information to customers such as Auto Delivery Time Estimate, Dispatch Time to create an urgency of your daily shipment schedule, or manually add time estimates right to each of your product pages, like is demonstrated in this post.
All the best,