If your having a UPS package delivered to a UPS store and the UPS store is open you should be able to pickup the package from the UPS store so long as you have the tracking number and your ID.
However it's usually best to just wait until it shows delivered to the UPS locker or shows that it's ready for pickup.
If the package is to be delivered to your door then if it's on the truck and out for delivery then you can't pickup the package and will have to wait until the UPS driver gets to your house.