A physical optical DVD drive?
No wonder it takes time to boot.
Due to the size of the ISO, the read speed of a DVD drive and the way a Manjaro ISO is constructed by using 4 overlay filesystems - booting from a DVD drive is known to be a very bad experience.
Use an USB stick big enough to hold the iso-file - use ventoy to make it bootable - then copy the ISO to the USB - no burning - drag’n drop the ISO onto the USB.
When your system doesn’t recognize Manjaro - then you have a system supporting EFI but prioritising MBR boot - thus your Mint is MBR and Manjaro is EFI - which is entirely possible but you cannot mix the two into a bootloader menu.
You will have to choose from your firmware bootoverride menu - accessible by pressing a function key during boot - F12 on a Dell system.