In case anyone was wondering, a tire is date stamped for when it was made. That's not saying it didn't sit in a warehouse for 18 months before it was sold, though.
Somewhere on the sidewall will be something like 'DOT 2315'. The DOT indicates it's a DOT specified code. The 1st 2 digits are the week of the year, the last 2 digits are the year. So, 2315 would have been made in the 23d week of 2015.