No. USPS cannot pick up your FedEx package. There were several times during my career as a mailman that we accidentally had a UPS box or FedEx box in our system, and eventually, we will get it back to the original carrier. But, since it wasn’t placed through the proper channels you can expect delays.
What will happen if I dropped off my FedEx package to USPS?
If that’s the case, you won’t see tracking for a while at least. That’s because your local post office is going to have to wait until the next time there is FedEx truck on the property dropping off or picking up packages to get it into their system.
If that’s your situation, I’m sorry to hear it. The only antidote is patience, without tracking it will impossible for anyone to locate it.