You may have to download the iso and burn it onto dvd.
Once done install to the ssd from the dvd drive.
Then after reboot plug in the usb drive and using the file manager create a folder for the gamea and copy the games it.
Otherwise boot clonezilla .
This will clone the entire usb drive
It might work but thats questionable.
You should be able to do a raw write on the SSD itself with the thr same Batocera ISO. You need another USB for this )or maybe just one USB if you have Ventoy installed in the USB).
Ventoy is an ISO launcher. You write it the same way as other bootable OSes. Then in the remaining disk space, you can put ISO
Im not sure if you could use the active ISO with other process/operations, so you probably need another OS to boot into and perform the dd command.
I dont know the exact syntax of dd off my head so I suggest you read the man pages (or read an online article" prior to this.