Yes a package can say delivered and not be actually delivered.
Sometimes I'll have a package through USPS say the package was delivered but it doesn't show up until a few hours later or the next day after it updates again.
Sometimes the tracking through USPS is not very reliable and sometimes a mail carrier delivering the packages may actually scan it as delivered before the package actually is delivered.
When your package says out for delivery then it will or should be delivered that day but if it's still in transit then it won't be delivered until the expected delivery date.
If you still have not gotten your package delivered then you should call your local post office with the tracking number and find out what happened to the package.
Sometimes a package may get delivered to the wrong address and they can then find it.