The "Anti-Theory" Thread

That's not a big problem. Sometimes people do have fragmental memories from their infancy. Leia didn't exactly remember details. It was just images and feelings. She must've had a quite stressful infancy to remember even that much, though. According to the novelization of ROTJ, Leia had vague memories of running and hiding.
I guess Leia simply stayed with Padme while Obi-Wan went into hiding with Luke. Then Padme had to hide from the Empire and was eventually killed. Bail Organa was probably with her and took care of Leia. Perhaps they were even on their way to Alderaan.