This guide allows you to softmod your PS2 fat model in easy steps without an existing FMCB card or any rom manager. Thanks to the Reddit user u/quisys for the original guide.
Disclaimer: make sure you know what disk you're writing to when using dd command, I am not responsible for any data loss.

Required Hardware

• Fat PS2
• Memory Card
• PS2 Network Adapter
• Controller
• HDD
• USB key
• SATA to USB cable

Required Software

• dd, exfat-utils, util-linux (you probably already have these in your distro)
• wLaunchELF KHN HDD image
• FreeMCBoot installer
• wLaunchELF 4.43x_isr
• OpenPS2 Loader

Install FreeMCBoot

• Connect your HDD to your computer, then write "__mbr.raw" (wLaunchELF KHN HDD image) to the HDD:
  sudo dd if=__mbr.raw of=/dev/sdX [Determine the path of your HDD using lsblk. It should be /dev/sdX, with X being the letter of your disk. ENSURE YOU USE THE PATH OF YOUR DISK! IT SHOULD NEVER BE /dev/sda]
• Unmount and remove the HDD
• Extract FreeMCBoot Installer then copy BOOT.ELF, OPNPS2LD.ELF and FMCBinst folder to your USB key
• Plug HDD and USB key into your PS2, then turn on the PS2
• Enter file browser, go to mass: and launch BOOT.ELF
• Enter file browser, go to mass: > FreeMCBinst folder and open FMCBInstaller.elf (not the exfat one), then select Install FreeMCBoot following the on-screen instructions. Restart your console
• Open wLaunchELF and go to file browser, go to mass: and hover over OPNPS2LD.ELF and press R1, select Copy. Go to mc0: or mc1: (depending on which slot your memory card is in), go to OPL and press R1, select Paste to overwrite OPNPS2LD.ELF
• Restart your PS2, open OpenPS2Loader, go to About and make sure the version is not 1.0.0, then turn off your PS2 and remove the HDD

HDD Management

• Connect your HDD to PC and format it in ExFAT (I suggest you a partition manager, or you can use mkfs.exfat /dev/sdX)
• Make a folder called DVD and a folder called CD in the root of your HDD
• Copy your videogames .iso to the DVD folder or your .cue/.bin to the CD folder

OPL Setup

• Plug in your HDD to the PS2, turn on your PS2
• Go to OpenPS2Loader > Settings and turn on cache game list (HDD), set BDM start mode to Auto
• Go to BDM Devices, disable USB, enable HDD
• Press OK, hit Save Changes

I still want to find a way to do this on my PS2, sadly I only have the slim SCPH-9001

Macho Macho has a guide on modding the slims, you've got options between FreeMcBoot on an SD card memory card (like the MemCard Pro or Ali clones), hard modding it, or using a NAS and the Ethernet port.

Obligatory "I need to update my OPL"

IT SHOULD NEVER BE /dev/sda

It could be, and it's even more likely now that NVME SSDs are more common and the HDD might be someone's only connected SATA device.

But better advice overall would be to use some GUI application for writing disk images. I know what I'm doing and even I don't trust myself to not have a brainfart when imaging a disk by its device path.

1. Get yourself an SD2PSX or BitFunx PSXMemCard Gen 2 (they're the same thing). I recommend these specifically since they support the MMCE protocol which allows you to load games off of them as well as loading the exploit and saving essentially an unlimited amount of games to a single microSD card. NHDDL with Neutrino is the modern day game loader that supports all of this.

2. Follow these instructions: https://ps2homebrewstore.com/exploits/tuna-sd2psx/

Using FreeMCBoot is a bit outdated now that things like OSDMenu exist, which is a modern open source replacement.

I'd recommend following this guide instead: https://ps2homebrewstore.com/exploits/

Also if you don't already have a memory card running the SD2PSXtd firmware, I would highly recommend getting one. You can load games and homebrew off of it through the MMCE protocol which is nice for slim models, you can have unlimited memory card images which will autoswitch when you load a game in NHDDL or OPL (NHDDL being the more modern game loader frontend built on top of the very lightweight and versitile Neutrino), and you can download pre-exploited boot images from the Internet so you don't have to go through any installation steps.