I am not sure if use of GRUB_DEFAULT=1>1 will work
GNU GRUB Manual 2.04: Simple configuration only mentions use of a single number
so GRUB_DEFAULT=1 will boot the 2nd ‘menuentry’ which should be the fallback initramfs
for the latest installed kernel
use this command to check the list
sudo grep ^menuentry /boot/grub/grub.cfg |cut -d "'" -f2
This is not a good solution for booting later ‘menuentry’ options as the ID number is more likely to change when a kernel is added or removed
I have not seen the Advanced menu included the name, as in post by @Hagen
only simpler examples of using menuentry name, lik this:
GRUB_DEFAULT="Manjaro Linux (Kernel: 5.10.7-3-MANJARO x64 - fallback initramfs)"
This is good to keep boot locked to one option, but /etc/default/grub would have to be edited when the kernel version number changes
I use the same options as @anon89812132
(GRUB_DEFAULT=saved and GRUB_SAVEDEFAULT=true)
But I add an option to GRUB to disable the Advanced menu, so It is easier to see the boot options and change which one I want to use
echo `GRUB_DISABLE_SUBMENU=true` | sudo tee --append /etc/default/grub