My theory: She was reincarnated to that child, but there was no one who could raise her - her grandpa got stuck in the past, because he lost the last stone and cats would not be able to do that. But he wanted to help her and was somehow able via those cats and one of them returned to past, grabbed ML and transfered back into future, where ML found the baby. There was probably also no energy left for more than 1 jump... otherwise: Her grandpa could get to future himself and raise her again and send to the past or ML into future when she is grown up and it would be HE.
Anyone know the ending of novels?
