I’m willing to beat that the little girl’s family gets killed by the Skullcrawlers (or maybe the bat creatures) just like Kong’s family. Maybe he fights them off but she’s the only survivor. He feels a bond with her because they were both orphaned because of Skullcrawler attacks.
Another movie theory. Godzilla wins the first fight because Kong by himself can't stand up to the atomic breath. Plus they're on the water which is Godzilla's home court. Second fight Kong makes a weapon to nullify the bad breath and wins because of his strength and speed. Without weapons he doesn't stand a chance but if he has time to plan he wins. Basically Godzilla is Superman and Kong is Batman. "Save Mothra!!!"