Cheeseburger Let's get our terminology straight, to avoid further confusion. The first step is not 'unlocking the OEM', but enabling OEM unlocking. This can only be done from within an OS, so yes: you do this from within the original OS. And this is the step which requires internet connection.
After enabling OEM unlocking, you will boot into the bootloader interface. You are not in the OS anymore. Then you will connect the device to the computer, after which the actual unlocking of the bootloader is done.
You can find all the information in the install instructions, please take your time to read and follow the instructions precisely. The technical language may sound difficult, but most users are very surprised at how easy it in fact is: https://grapheneos.org/install/web