On the individual package, for any First Class, Priority Mail or Priority Express Mail package, the cost of tracking is very low. It is only $1.05 directly at the post office counter, or you can add it to your online purchase for $0.23.How can I track my USPS package without a tracking number?
If the shipper sent you a confirmation email, there may be a link in there you can click on to track the package. In fact the email might even contain the tracking number! Otherwise, no. There is no way to track a USPS package without a tracking number.