Lelouch would be a likely candidate. He has a strong sense of justice and a desire to change the world. Given his intelligence and strategic mind, if he were to discover the means of time travel, he would likely use it to correct the many wrongs in the Code Geass world, such as the oppression of Britannia. He could go back in time to prevent his mother's death and change the course of his own life and the fate of the world.
C.C. might also be a possible character to start time travel. She has a mysterious past and a deep connection to Geass. Since she has lived for a long time and witnessed many events, she could use time travel to fix some of the mistakes or tragedies she has seen. Maybe she wants to prevent the misuse of Geass or change the way the world has developed due to Geass. Also, she might have some knowledge or power related to time travel that we don't know about yet in the original series.
Lelouch is a very likely candidate. Given his intelligence and his desire to change the world, time travel could be a means for him to correct past mistakes or gain more power to overthrow Britannia. Another one could be Suzaku. He has a strong sense of justice and might use time travel to prevent some of the tragedies that occurred.
Well, in 'Code Geass Time Travel Fix It Fanfic', a cool concept might be the butterfly effect. When a character time travels, even the smallest change they make can have huge consequences. It could be something as simple as saving a single person who then goes on to change the course of an entire battle. Also, there could be the idea of self - discovery through time travel. A character might learn more about their own powers or purpose in life by going back and reliving certain events. And then there's the concept of rewriting history to create a better future for everyone, not just the main characters.
Batman himself is a likely candidate. Given his intelligence and determination, he might stumble upon a time - traveling device or technology while investigating some strange phenomenon. He would be driven by his need to protect Gotham, perhaps by preventing a future catastrophe that he has foreseen.
Star - Lord is a likely candidate. He's always been a bit of a risk - taker and his curiosity might lead him to experiment with time travel technology.
Koro - sensei could be a likely candidate. Since he has advanced abilities, he might be able to figure out time travel in some way. He could use it to try to change his own past or to better prepare the students for their future.
The relationship between the Black Knights and Lelouch would also change. If Lelouch goes back in time and is more strategic from the beginning, the Black Knights might be more unified and loyal to him. They would see his long - term vision more clearly and be more willing to follow his every command, which could lead to a more powerful and efficient resistance against Britannia.
Time travel can greatly expand Lelouch's character development. When he travels back in time, he gets a second chance. This makes him more cautious as he doesn't want to repeat the same mistakes. For example, he might be more careful in his relationships with Suzaku and others, knowing how things turned out before.
Another possibility is that Kallen travels to a time when the Geass power was first discovered. She might get involved in the events that led to the creation of the Geass and try to change the way it was used. Maybe she could stop certain individuals from getting Geass powers that were misused later. This would change the whole power dynamic in the Code Geass universe.
There is a fanfic called 'Lelouch's Time Travel Adventure'. In it, Lelouch travels back in time to a point before the start of the series. He uses his knowledge of the future to try and prevent the events that led to the sad state of the world in the original story. It has some really cool moments where he outsmarts his enemies using future knowledge, and the way the author writes his internal monologues is very interesting, making it a great read for Code Geass fans.
One way could be through some sort of wormhole encounter. If a flight accidentally flew into a naturally occurring wormhole during its journey, it might be transported to a different time. Wormholes are theoretical shortcuts in space - time, so a flight entering one could end up in the past or future.