No you cannot track your mailman.
Your mail carrier cannot be tracked by the postal customer waiting on mail or packages.
However the postal vehicles likely do have GPS on them but only for the USPS to use to track the mailman and mail truck.
The only thing you can track is your package through USPS.
If your package is out for delivery that day then the package will say out for delivery.
Amazon has a way to track the UPS driver or Amazon delivery driver that is delivering to your door.
However USPS does not have that option available to customers.
But if you're waiting on a package and it says it's out for delivery then you will get the package that day.
If it does not say out for delivery then you will get the package the next day if the package has reached your local post office.