You can't. At least not generally, and not through a general file manager like dolphin. That's the whole purpose of mounting; to make the file system and its contents available to the operating system. To bypass mounting, you'd have to have a program that reads the drive directly and have some way to parse the bits you get out of it.
One possible option, for example, would be with the mtools package. These are command-line programs that are designed for accessing FAT filesystems directly. But even these were designed for use when FAT floppy disks were the most common data medium.