Take it to the movies or to a nice restaurant...

Oh, you mean that sort of date...

I tend to remove the cover and look at components, they are often date marked inside - inlet solenoid valves in particular often have a manufacture date stamped on them. Also sometimes the detergent dispenser casing might be date-stamped, or the drain pump, just look around under the hood for date stamps. It's very common to have date-stamped components.