Yes a brand new car battery should come fully charged.
When you buy a new car battery and install it you should not need to charge it up before it starts your car.
The battery should immediately start your car up after installing the new car battery and if it has lost it's charge then the battery is likely not good anymore and you should return the battery to the store you bought it and get another new battery.
Every battery I have bought new for my vehicles were charged up enough to start the vehicle without needing to charge it beforehand.
So you should be able to just install the new car battery and then start the vehicle right up and after you do then you should drive around for a few minutes to put the charge back into the battery after starting the vehicle.