'Where is my order' is one of the most common support enquiries in e-commerce, and one of the easiest to reduce with a small number of well-timed automated updates. Order confirmation, dispatch, and delivery are usually the three moments worth an automatic message, enough to keep a customer informed without over-messaging them.
The wording matters as much as the timing. An update that includes a specific detail (an estimated delivery window, a tracking reference) answers the question before it's asked. A vague 'your order is on its way' often prompts the exact enquiry it was meant to prevent.
Allowing a reply on the update thread, rather than sending a one-way notification, also helps, a customer with a question can ask it immediately, in context, instead of opening a new support request.