First Time Mom— Nighttime

Hello everyone! Our perfect baby arrived about a week ago and we're so in love!

I was wondering if anyone had any advice — I'm scared to fall asleep, l'm scared I'll fall asleep and not hear her cries at night.

My husband falls asleep around 3am and he tells me that I should take advantage of when baby is asleep to sleep myself— even the pediatrician told us to sleep when she sleeps, but for some reason I get anxious that if I fall asleep, I won't hear her cries There's times where she gets fussy, even after we change, feed, and coddle her, but she just whines and eventually falls asleep on her own. Do you all wait until your little one cries to pick them up or do you grab them when you hear them fussing? And if anyone has any advice about my anxiety of falling asleep, that would be appreciated!

Thanks all!!!! God bless all of you