
FMCB does take quite a lot of space on the memory card though. Probably want a second one for saves.FMCB works by exploiting a flaw in a sort of 'update' that memory cards could apply to the PS2. The only options are installing it onto a memory card or using a network adapter and installing FHDB onto a HDD. You should have a memory card anyway since it's required if you want to save your game (Installing FMCB doesn't make the memory card unusable for saving data to if that's what you're worried about). And yes you can load games off a USB using OPL, but it is known for having slow loading times due to it being USB 1.1. If you don't mind the loading times then it should be fine.
There are a few ways to get it installed, but the most recently released method is probably the simplest if you are on a supported PS2.
https://github.com/CTurt/FreeDVDBoot
Found this while googling your question: Yes, but there are problems with doing this. The USB ports on a PS2 are USB 1.1, which means they are very outdated and slow. The transfer speeds are slower than from the disc and the load times will be long, there may be stuttering, and games may even freeze. If you have an old "phat" model PS2, it would be a good idea to install a hard drive.
Edit: You can use an SD card with some converters also.
Optimal Shop Secure Digital SD SDHC SDXC MMC Memory Card to IDE 2.5" 2.5 Inch 44P 44 Pin Male Adapter Converter, SD 3.0
Generic SATA/PATA/IDE Drive to USB 2.0 Adapter Converter Cable
A Phat PS2 network adapter.
2.5in to 3.5in IDE Hard Drive Cable Adapter
Here is a video if you want to sit through it.