Arch recently moved legacy Nvidia support to the AUR. That might have left you with a broken install.
You would probably have an easier time with a mainstream distro like kubuntu LTS. They tend to be better suited for older equipment.
It can be challenging to fix the bootloader once it dumps you into this situation. On a UEFI secure boot installation the EFI shim is responsible for allowing the modules to load each time there's a change.
If you have a legacy MBR installation the Nvidia modules might just need to be reinstalled. This was a common issue when updating the kernel.
Edit: switching it to the Nouveau drivers might get you back into the OS. Would need to tweak your environment from a working one with a live environment potentially.