I just setup a MoodleBox with a Raspberry Pi 4B and an USB SSD 240GB. You can take any external USB SSD. But you also can use any internal SATA SSD for PCs together with an USB 3.0 SATA adapter. I got my adapter for 8 Euro from A........
I copied the current MoodleBox image 3.12.0 to the USB SSD using the Raspberry Pi Imager 1.6.2. https://www.raspberrypi.org/software/. Then I connected the USB SSD to one of the blue USB ports of the Raspberry Pi 4B. The blue ports are USB 3.0 and the black ports are USB 2.0. There was no microSD card in the Raspberry Pi 4B. I switched on the power and the MoodleBox started from the USB SSD automatically. Everything works fine. I also tested the USB SSD with a Raspberry Pi 3B+.
You will find more infos for USB mass storage boot on Raspberry Pi. A new Raspberry Pi 4 and a Raspberry Pi 3B+ are supporting USB mass storage boot out of the box. On earlier Raspberry Pi 4B boards the boot loader must be updated. On the Raspberry Pi 3A+ and 3B you must first enable USB host boot mode.
I hope you will get it.