Is a SD card necessary to do firmware update?

no you can use you device to plug into the drone or download the dpi assist app and connect your drone to your computer to do it, it will also do it wirelessly.

Actually there is no way to update the P4 firmware using an SD card.  That was a P2/P3 thing.

If your phone or tablet is connected to the internet, you can upgrade using the controller.  When a new firmware version is released, you'll get a notification pop up on the screen.  When that happens, just follow the further instructions you get on your phone or tablet.

OR as mic75 says, you can use the DJI Assistant 2 application on your home computer.   (I prefer to do it this way as I feel I have more control over the process).