The only way I know of would to be to cut a small section off of one of the ends and then dissect it.
Inside of the sheath next to the core strands should be a tracer thread and identification tape,
During the braiding process, an identification tape
and tracer thread indicating the year of manufacture
are woven into the rope core.
The year of manufacture tracer thread is made from
polyamide, and is in a particular colour. Its colour
shows the year the rope was manufactured, although the same set of colours is repeated every ten
years. The year of manufacture tracer thread means
that this information is permanently marked for the
lifespan of the rope.
The identification tape is a thin strip of polypropylene. In accordance with the EN 1891 standard
for static ropes, it has to display the following information: name of manufacturer, standard and rope type, year of manufacture and the type of material
the static rope is made from.
The identification tape should say the year right on it, and I have seen this before when I was decoring retired climbing rope to make rope bracelets out of it.
You would have to contact the manufacturer in order to find out what year that color of tracer thread was used.