Irina Jelavić could be another possibility. As a professional assassin, she might have access to some secret technologies or knowledge that could be related to time travel. She could use it either to complete her mission of assassinating Koro - sensei more effectively or to save the students from a bad future she has foreseen.
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.
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.
Ciel is a likely candidate. Given his intelligence and determination to avenge his family and protect his future, he might see time travel as a means to change certain events in the past. He could use it to find out more about the people who wronged his family and stop them before they act.
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.
It could be Nagisa. Since he is one of the central characters in the original series, he would make a great time - traveling protagonist. He could travel back in time to gain more skills or knowledge to better assassinate Koro - sensei, or he might go forward in time to see the consequences of their actions in the classroom.
Eleven could be a likely candidate. Given her powerful psychic abilities, she might accidentally or purposefully time travel. Her powers have always been a bit unpredictable, and time travel could be an extension of that. She has a strong connection to the Upside Down, so she might be sent back in time to learn more about its origin or how to stop it.
It could be Louis. He has always seemed very connected to the group's roots. In fanfiction, he might realize how much the fans miss the band and how much they all still have in common musically. So, he starts reaching out to the other members one by one to see if a reunion is possible.
Goku would be more likely. He is always open to new friendships and challenges. He has a curious nature and would be intrigued by Kefla's power. So he might approach her first to test her strength or just out of friendly curiosity.
I think Ruby and Nagisa would be a great pairing. Ruby is all about being a hero and has her own sense of justice, while Nagisa has been trained to be an assassin but also has a good heart. Their different outlooks could lead to some really interesting conversations and adventures.
Naruto himself would be really interesting. His never - give - up attitude could inspire the students in the Assassination Classroom. He could also learn from their unique skills and knowledge. His journey in this new world would be full of surprises as he tries to adapt to their assassination - based curriculum.