How can I find the time since a Linux system was first installed, provided that nobody has tried to hide it?

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/syslogfor 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.)