when to let baby learn to self soothe?

Ms
My baby will be 2 weeks old tomorrow.
I keep telling my fiancé that I'm exhausted because I get up every hour at night with her. At night she likes to cluster feed, and she uses me as a human pacifier to help herself fall asleep.
As exhausting as it is I really don't mind...she's still a newborn and she won't do this forever.
He says that I should just let her cry and only get up every 3 hours to feed her.
I say he doesn't understand what a baby needs. She is far to young to let her cry it out.
Not to mention she co-sleeps with us. Her crying doesn't wake him up; but I wake up every time she makes a sound...i still wouldn't get sleep if I let her lay there and cry.
When do you guys think it's appropriate to start letting her learn to cry and self soothe?
I think she is far too young. At this age when she crys it's because she needs something, and she needs to be tended to