Date A Devil! Mac OS

If the computer's drive has not been reformatted and no Archive & Install
or reinstall actions have taken place on the computer, the first install and
run-up event should be in some of the system's logs; failing that, but still
no major changes in the computer, the oldest date found in Get Info on
the computer's hard disk drive (there would be two, first initialization or
format for use of the drive in the Mac, and second, Modification Date)
as the approximate date of installation.
(You can highlight the Macintosh HD icon and choose Get Info for these.)
There should also be other dates, however they may have been wiped
or changed if anything was done in the System where utilities had been
used to modify logs or cache histories. Tools such as OnyX & others can
be used to wipe these kinds of data histories from the computer.
If the hard disk drive has not been wiped, nor the creation date of any
partitions made for that installation, an approximate date may be found.
Disk Utility may be able to find some relevant information, probably not
too different than that found by Get Info. And lastly (perhaps first) use
of the Console utility in the Utilities Folder, may be able to show you a
log of all activity; the oldest dates of plausible likelihood may be the one.
The most recent installation and modification dates should be apparent;
and any previous system info, should a complete reformat have been
done and a new full install performed, would be gone from your view.
Since dates of changes made to the system would be newer than the
first original installation, many other dates and changes each time a
software update or new App, a widget, or Disk Utility's 'repair disk or
repair disk permissions' were run, would offer a newer date.
These are possible leads. If I had the MacBook/Pro here, I could find
the date common to the first OS X run of the current installed system;
but if it were a clone, the date may not be of that earlier event.
Console logs cover many aspects of the system and what runs within it.
So, that may be a place to look. And there are several kinds of logs.
Good luck & happy computing! 🙂