is your SIP disabled and is your HDD/SSD formatted APFS and yes you should create a macOS Catalina usb patcher that if you don't have the SIP disabled you can boot into the usb Catalina Patcher enter in the terminal csrutil disable and as far as I know if your HDD/SSD is not APFS you can formatted it APFS and install Catalina without having to use the APFS boot rom patcher which can be risky
cant remember if SIP is active or not. Disk formatted for AFPS with an EFI boot loader in front of it (from when I put either 10.12 or 10.13 on the machine)
Went in to EFI shell, swapped to fs0 and manually executed startup.nsh which has (thankfully) booted me back into the OS.
Going to create a USB installer and go from there. Cheers