How do I find how long ago a Linux system was installed?

sudo tune2fs -l /dev/sda1 **OR** /dev/sdb1*  | grep 'Filesystem created:'

This will tell you when the file system was created.

* = In the first column of df / you can find the exact partition to use.

Check the date of the root filesystem with dumpe2fs. I can't really think of how that could be anything other than the date you're looking for:

dumpe2fs $(mount | grep 'on \/ ' | awk '{print $1}') | grep 'Filesystem created:'

There are a few dates lying around.

• All files have dates.
• Log files have dates in them.

On Debian or Ubuntu and their derivatives, see /var/log/installer/syslog for the definitive answer if it exists it is part of the log of the instillation.

But beware this is not guaranteed. (see other answers/comments for some of the reasons it may not work.)