Try upgrading to macOS 10.11 El Capitan first. I've seen reports where this intermediate version of macOS may be required perhaps because of a system firmware update. Install macOS 10.11 and make sure that all available updates are installed before attempting to upgrade to Catalina.
I recommend you create a bootable macOS 10.11 USB installer (read the instructions very carefully on how to extract and install the El Capitan installer to the Applications folder):
https://support.apple.com/en-us/HT201372
https://support.apple.com/kb/HT206886
I also highly recommend that you have a good verified working backup before performing the OS upgrade just in case something goes wrong. You should always have frequent & regular backups. FYI, it is impossible to recover accidentally deleted data from an SSD. Plus an SSD can fail at any time without any warning signs.