... I assume the idea is let them cry for x minutes, then go in and soothe to stop the crying, then let them cry for x minutes, right?

What happens if they *don't* stop crying when you soothe them? Is the idea to say "there there, mommy's here", or to give them a crying respite?

I ask as I'm struggling with how to push back/eliminate LO's first night waking. I always give her her paci first and try to rock her to see if she'll fall back asleep (and if she would, I'd assume she's not hungry, but just waking out of habit, so then the NEXT night I can let her CIO or whatever). It's never happened, she usually just keeps crying until I feed her. I assume if I tried to do intervals, she'd just cry and cry because soothing does nothing.

Do I just assume she's hungry? Or do your LOs cry through the soothing and eventually just fall asleep?