This is clearly not the case, in the image above you have a booted system that appears to be installed, and are mistaking no graphical interface for not booted.
I think going for a more beginner friendly distro is honestly a better option for now, don’t take this the wrong way, but you will have issues.
Feel free to use it if you really want to, no-one is going to stop you, but you won’t have a good time and “issues” like this will be ongoing.
With all that out of the way, get used to using a terminal constantly.
Post me the output of the following
pacman -Qs lightdm xorg-xinit
And tell me what choice you made during install (I only care about which login session and packages you chose, partitioning and other choices aren’t important in this case)