Whenever I first install Solus Linux, the installer never adds Solus to the UEFI Boot Menu. Here are the steps to fix that issue:

Boot from your live CD/USB. Connect to the internet, and do the following:

Install efibootmgr: sudo eopkg it efibootmgr

(This paragraph probably isn’t necessary, but I am including it to remember how to clean up the UEFI Boot Menu 🙂 )
Run efibootmgr with no arguments. You should see an entry for Linux Boot Manager, which for some reason doesn’t show up in your actual boot menu but does here. There’s a number listed for that entry. Delete it with sudo efibootmgr -b [num] -B

Now you can recreate it. If your EFI partition is /dev/sda1 then do this: sudo efibootmgr -c -d /dev/sda -p 1 -l "\EFI\systemd\systemd-bootx64.efi" -L "Linux Boot Manager"