The RPi3B+ already allows for USB booting, so that's a good start. Hopefully your USB-SATA adapter is capable of fit for booting.
It also means there needs to be a system partition on the SSD for the RPi to boot from.
Option 1
The 'simplest' solution would be to copy the current contents of the SSD to a temporary external location (a Linux PC?), then write the LibreELEC image onto the SSD so both partitions are created and LibreELEC can boot from it, and then restore the entire storage contents back to the SSD.
Option 2
"Without destroying existing data" is not impossible, but you will need a tool like GParted, to shrink and move the current EXT4 partition on the SSD to make room for the 512MB/1024MB size EXT4 system partition. Moving partitions around on a SSD is not their favorite actions AFAIK, but it's doable. Then copy of files from the LibreELEC SDcard's system partition to the SSD's system partition, hook up the SSD onto the RPi3B+ and power it up. And hope it all works
If the current disk format on the SSD for storage is not EXT4, then option 1 is still the required option.