Without the tracking number, you won't be able to receive the order information; however, you may use USPS
Informed Delivery. This service allows you to preview parcels before arrival via gray-scale photographs of the items and their labels. It also allows you to manage packages and track all the shipments without the need to enter individual tracking numbers.
To take advantage of this service, you will need to create a personal account. The service is only available for eligible ZIP Codes.
If your order was sent through Priority Mail Express, you can ask for the tracking information in the nearest postal office.