There are quite a few games with the mechanism you're talking about. I've highlighted a few here, ordered chronologically:
The beginning of 1993's Day of the Tentacle lets the player alternate freely between its three protagonists in three different time periods.
In that same year, Sony Interactive released Sonic CD. By speeding up for a certain amount of time, Sonic is able to travel the same level at different times: the past, the present, and a good and bad version of the future.
Getting close to the specificity of the dimension-shifting ability you are referring to, a game that uses a technique similar to that in Guacamelee, is 1999's Soul Reaver. As the protagonist Raziel, you can switch between the material plane and the immaterial spectral plane, where time flows differently.
After searching for what you referenced from Titanfall 2, I don't get why Respawn gets so much praise for their mission 'Effect and Cause', as I have seen that instantaneous time-travelling mechanism a few times before. The less known Singularity, a game released in 2010, has the exact same mechanism at its core. It even included an almost identical time-manipulating device, worn on the left hand.
I think I have seen this more often, although in most cases purely as a storytelling device, but I can't think of another title at the moment.
Other games that have similar time-manipulation as a core mechanism, include Braid, Prey (2017), Quantum Break, Prince of Persia: The Sands of Time, Blinx, and Life is Strange. (For more games, check out these lists on Steam, Wikipedia, or TVTropes.)
The first game to use a time travel mechanic as listed by this Wikipedia article, is 1980's appropriately named Time Traveler, a text adventure that has the player travel to different times in the past, but this might not fit your description, as it doesn't involve interactive shifting to solve puzzles.
In that same looser interpretation, the entire idea of being able to save your game is a variation on this theme. That concept alone could account for the development of time-manipulation as part of a game's in-universe gameplay, and as a possible 'origin'.