Sometime after protecting Fabul, Cecil, Yang, Edward, and Rydia set sail for Mysidia. Out of nowhere, a wild Leviathan appears in the sea. He attacks the ship, knocking Rydia overboard. Yang dives in to save her but to no avail. Leviathan swallows her whole.
We assume she’s died. However, she appears once more, as an adult, in the fight against Golbez. But how? Apparently, she’s aged in Freymarch, the Land of the Summons. But then, how did she get there? Didn’t Leviathan consume her? Rather, more like protect her. At the time, she was only eight. She would be far too young to survive the trials that await her. The dangers she would have to face are too much for a child. Imagine eight-year-old Rydia against Golbez.
She’s also one of the last summoners of Myst. Without her, the Eidolon’s connection to the world might vanish. Hopefully, she can have children to secure the summoner bloodline. The only way to do this is to keep her safe.
Rydia knows black and white magic, but she has no summoning powers. Leviathan felt it was appropriate to take the child and train her. Her sacrifice would result in losing the ability to cast white mage, but now the Eidolons have a connection with the world. Hopefully, she can have children to secure the summoner bloodline. The only way to do this is to keep her safe.
But then, how did he appear in the sea, without being summoned? That’s unclear. Note that when Rydia suffers stress, Eidolons come to her aid without her having to directly summon them. The first was Titan. When Cecil and Kain tried to abduct Rydia, Titan appeared. Perhaps her latent powers activate subconsciously, through her emotions. In the same manner, Leviathan appears to aid her. Of course, he wanted to train her to control her powers. Obviously, he’d rather her not summon him and others when she’s afraid of spiders.
However, he also need Rydia for one more important task: acquire Bahamut. While the plane of existence appears to be beyond space and time, the portal to Freymarch exists underground. Bahamut resides on the moon. He needed to find a way to contact the king of the dragons, and he did so through Rydia. He trained her to hone her powers with accuracy. He also made sure all of the pieces would fall together naturally.
Rydia couldn’t do it alone. In Cecil, he saw a competent warrior. Leviathan can use the seas to his advantage. Instead of drowning them, he saved Edward, Yang, and Cecil. Perhaps the other crew drifted to shore safely. It all worked out for the best. Cecil landed in Mysidia, where he would find redemption. With at least one of these people saved, Rydia could battle Bahamut, making him her Eidolon so that Leviathan could commune with him as well.