This is a good question and it would really depend on which courier you're using to deliver your products. Can you let me know who you're using and we can take a look into the different ways they track packages? There are some other general ways used to track packages without a tracking number which you can see here also.
If you are a merchant shipping with one or a few couriers, you can log in to your account. Normally, you can view the status of all packages that you've sent. If you have a Shopify store, the best way to keep track of the whereabouts of the packages that you've sent is by using app order tracking app like ParcelPanel, which can automatically pull tracking information from over 1,090 carriers worldwide for your business. It also allows your customers to access real-time tracking updates by using their email address and order number.
If you are a consumer who shop online frequently, make sure to take advantages of various services provided by couriers. Nowadays, many couriers allow you to subscribe to email/SMS notifications, and they have developed apps for you to send and track packages conveniently. There must be certain popular couriers in your country/region. Just subscribe to the tracking services and download their apps. What's more, smart package lockers at your residence can also trigger such notifications, provided that the deliverymen put your packages in such a locker.
Make Post-Purchase the Best Part of the Customer Experience. Delight your customers with automated shipment tracking, increase brand loyalty and drive more sales. Official Website | ParcelPanel Shopify App