Idea is nice, but time travel to the past is IMPOSSIBLE.
However, time travel to the future IS...great idea!
Lets say u r playing at 1000AD, suddenly u trigger some alien tech that can warp ur civ to 2000AD o_O . Ur archrival were still there , but now he has modern weaponry: mech, tank, gunship... While ur civ only have a horde of horse archer!
Fear strikes ur people , as he began to march his modern army toward ur border... It was the first time ur empire ever encountered such a unit called tank. The bloodiest battle was with the Indian's elephant rider, where your troops addressed them as 'The Mighty Trunk'... Now, the battalion of tanks rolled through your soil, u were shocked to realize that a single unit of tank massacred 5 of your elite phalanx guard!! The situation is critical now...
Suddenly, the sky roared! A 'giant roaring bird' flew overhead, its body was painted with a symbol that u recognized as one your neighbour's. A few shots, the enemy tanks was destroyed!! U have got an ally..
The world of 21 century got something call United Nation. Luckily, the secretary general of UN is a peaceful guy, so he demanded your archrival to stop his aggression and offer military assistances to this war. Over time, all other civs began to bind good relations with u. Open borders were signed.
-No bad relations from other civ
-Other civ tend to offer aid
Although technologically backward, your civ is an ancient artifact that warped from 1000 years ago, a live history ! Scientists from all over the planet began flocking to ur civ to investigate the "warp point". Historians began their studies on your civilization, new historical facts spawned as they study through ur empire. More and more people wanted to join ur interesting empire...Artists, archeologists, ecologist...
-500% Great people birthrate
-1000% Culture generation
EDIT the story abit