GPT and MBR are partition systems, and FAT is a file system.

You first need to create the partition system in the drive or USB you want to use, so you can create partitions, and in those partitions you can create the filesystem. This way, you can have multiple partitions with different filesystems.

The file manager will only show the device if it has filesystems that it can open, I guess that is why it does not show you anything.

I think there is way to create a partitionless drive, but I think it's better to just do it the usual way.

I recommend you to use GPT, by the way. Hope this helped.