If the USPS package is at your local post office where mail is delivered to you and it is still at the USPS then you can sometimes go to the post office as long as they are open and pickup the package before it is delivered.
If you get USPS packages or mail delivered from your post office to your home address and the mail is not out for delivery yet then yes you can go to the USPS and pick up the package.
However if the package is already on the USPS truck out for delivery then no you won't be able to pick the package up until the USPS driver gets to your address and delivers it to you.
I just wait until the package is delivered to my address instead of worrying about picking it up though because nothing I have ordered is that important that I have to get it right away.
But you certainly can go to the post office and get your package before it's delivered to you if it's there and not out for delivery yet.