About the installation of i3 alongside XFCE

I cannot install i3wm directly into my computer because of the kernel. As of now my laptop only boots up in LTS kernel. The only lts kernel garuda has is in XFCE editon. And my concern is can I install i3wm alongside with xfce. Or is there better way?

Install i3wm, chroot, install needed kernel. Done.

The usb doesn't boot up with i3wm in the first place.

Yes you can.
If you want garuda i3 settings, you can install the appropriate settings package (use pacman -S garuda-i3-settings, or copy the settings from Gitlab).
After i3wm installation, if you use a DM (LightDM etc.) choose i3 session from session selector combo. Else you add proper exec i3 command in $HOME/.xinitrc