Okay in any fulfillment operation tracking occurs when an order is placed. You need to know when a label is printed, often when specific items are packed, and when that order leaves the building. Bigger operations will have more steps for the fulfillment chain and delivery if they do that part.
From a customer perspective, even your mom and pop shop doing UPS pickup will create a label with tracking so the customer knows when their shipment has entered the delivery chain.
Am I misunderstanding what you are talking about?
I don’t know your shop. Everywhere I’ve worked when an order is placed there is an order ID and fulfillment ID and shipping label created automatically, so the order status can be tracked both internally and externally.
At any scale without these you’ll never be able up identify errors in the process.