Sure, you would need a trigger that is activated by owning a wonder. When activated it can then start a timer that will declare victory after a time period you define. You won't see a countdown of the time, unless you tigger additional timers to send chat messages with the countdown time periodically.

What trigger condition should I use to activate the trigger when a player owns a wonder? The attribute list in the "Accumulate Attribute" condition doesn't include wonders, only relics etc...

Oh, apparently there is a way to acheive this using the "Own Object" condition. I had contemplated that condition as an option before, but for some reason I couldn't find wonder in the object list! Thank you, Zetnus, for your assistance! Wasn't so hard after all :)

By the way, do you know if there's a way to make a visible "count-down" without having to make a separate message for every single year?

The own objects condition is the way to go.
I'm afraid I don't know how to do a visible countdown .... hmm
If you set a time limit for your game, that displays a countdown but I don't think you can activate or deactivate that at will, and you want it linked to the wonder not to the game time.
Maybe someone else knows how to do this?

There's no visible countdown unfortunately. You could display a message every 50 years or so though, that would be more convenient than displaying one every year.