Serious mom advice for a fussy 6 week old

I need some advice on the "cry it out method" my son is 6 weeks old and im having trouble getting him to sleep anywhere but on his stomach on my chest. Ive read that crying it out does not work for new little ones and ive read that for some it works he makes me feel terrible when he is crying so i pick him up get him to sleep and put him back down only to have him wake and scream again. Should i let him cry for a while? If so is there an amount of time i should let him before picking him up? Any other advice on what to do so i can get some sleep welcome as well