on archlinux, to see when you installed arch on your computer, run this command
sed -n "/ installed $1/{s/].*/]/p;q}" /var/log/pacman.log
it will display the date and the time when you ran pacstrap on the live cd to install your system.
on my laptop, i get [2018-10-21 21:05] , which is when i switched from fedora back to arch because my school required fedora.