@Nerces44 I use a NESPiCase4 with a SSD Disk. All my stuff (recalbox & roms) are on the SSD and I have no problem. Perhaps, that's an issue from your power adapter (not enough ampere) or an issue from your sata bridge firmware. I had to change the firmware for booting from ssd. Since I've done that my sata bridge seems to be more efficient (see http://download.retroflag.com/Products/NESPi_4_CASE/How_to_boot_from_SSD.zip).
@Nerces44 I forget... because of an issue with the NESPiCase sata bridge, you have to follow the following link from Retroflag: http://download.retroflag.com/Products/NESPi_4_CASE/How_to_boot_from_SSD.zip . I chose to flash the firmware...
If you don't have enough technical knowledge, please use the official method for installing Recalbox.
@acris You're right, it's not an official way of installing Recalbox. You must have some technical knowledges for understanding what you do and troubleshoot your system yourself... and a backup of your roms ! 
@Nerces44 Like you I use the official Raspberry Pi 4 power supply (3A) because the one from Retrolag is useless in my country (France).
For booting from SSD, you have to flash the Raspberry pi 4 firmware. You can find a lot of websites talking about it.
For flashing the img file on SSD, It's the same method than with a SDCard: I use the app "Imager" from Raspberry (but you can use another tool) and I select the SSD as target.
As Recalbox will boot from the SSD instead of SDCard, you have to change an option in a file named cmdline.txt in RECALBOX partition:
change:
dev=/dev/mmcblk0p1
by:
dev=/dev/sda1
That's all ! But... take care when you will upgrade Recalbox because it will replace cmdline.txt and you will have to change again the option dev=... . I've opened an issue in gitlab ( https://gitlab.com/recalbox/recalbox/-/issues/1373).
@Nerces44 I use a NESPiCase4 with a SSD Disk. All my stuff (recalbox & roms) are on the SSD and I have no problem. Perhaps, that's an issue from your power adapter (not enough ampere) or an issue from your sata bridge firmware. I had to change the firmware for booting from ssd. Since I've done that my sata bridge seems to be more efficient (see http://download.retroflag.com/Products/NESPi_4_CASE/How_to_boot_from_SSD.zip).