Time traveling and a certain pair of goggles.

[Enkidoh]

Except we did affect certain events and actively took items from the past into then present 1.0. During the 1.0 quests "Flowers for all" and Court in the Sands" we are tasked with taking a Velodyna Cosmos to the Goldsmithing (or was it Alchemist?) guild as it was a rare flower that was from then Garlean occupied territory of Ala Mhigo. We take it to the guild in question and are about to sell it to an excited merchant when the echo takes hold and we slip back into the past and sell it for a pittance as it is not "rare" in the current time. We receive said flower from the Parade in Ul'dah in the year 1562. Roughly 15 years before the setting of 1.0.

Except that was already explained by Ferne back on the old 1.0 forum that the original starting nation storylines in 1.0 were almost entirelly taking place within Echo visions. Most of the beginning of 1.0 you were not living those events as they happened, they had actually occured about 10 years prior when the Archons first arrived in the citystates, but you were bouncing about in and out of other people's memories with the Echo out of chronological order so it all ended up a confusing mess (the item you get in each of the citystates may have appeared within your inventory even outside of the Echo, but that was simply gameplay pragmatisim as it was needed to flag the next part of the storyline to execute and is not something deeper.). In 1.0's starting city story entering the Echo was almost undetectable, merely signified by a subtle 'gong' and woosh effect, so a player would not have even picked up on it at the time if they were not already knowing what to look for.

There was certainily no indiciation anywhere in 1.0 of literal time travel being an aspect of the story - the scene with Cid's goggles as I mentioned was not time travel back to the Sixth Astral Era, but the player's character 'hacking' Cid's mind in a way and lifiting the veil of amnesia that clouded him, restoring his memories, which was symbolized by the player's character handing him his goggles within his memory - it was for all intents an purposes, a delusion, in that it never literally happened.