To find out the Linux install date, there is no one single solution according to the Linux distribution type and version, there are some common ways to get the Linux OS install age.
Perhaps the most popular way to get the OS installation date and time is to check out when the root filesystem ( / ) was created, this can be done with tune2fs command

server:~# ls -alct /|tail -1|awk '{print $6, $7, $8}'
sep 6 2012

root home directory is created at install time

server:~# ls -alct /root

root@server:~# ls -lAhF /etc/hostname
-rw-r–r– 1 root root 8 sep  6  2012 /etc/hostname

For Debian / Ubuntu and other deb based distributions the /var/log/installer directory is being created during OS install, so on Debian the best way to check the Linux OS creation date is with:

root@server:~# ls -ld /var/log/installer
drwxr-xr-x 3 root root 4096 sep  6  2012 /var/log/installer/
root@server:~# ls -ld /lost+found
drwx—— 2 root root 16384 sep  6  2012 /lost+found/

On Red Hat / Fedora / CentOS, redhat based Linuces , you can use:

rpm -qi basesystem | grep "Install Date"

basesystem is the package containing basic Linux binaries many of which should not change, however in some cases if there are some security updates package might change so it is also good to check the root filesystem creation time and compare whether these two match.
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