The Ultimate “How to Sleep Baby” Question...

SO, we have been trying to teach(!) our baby to sleep on her own in her crib for the night. It has been 3 days buy still she is fighting after 40 mins and 4 consecutive sleepless hours. We follow our typical routine, darken the room, put white noise on, put pjs& sleep sack, feed, burp etc... and we put her in her crib while she is still awake but drowsy... HOWEVER unlike all sleep training books, blogs, etc say, she can’t go to sleep on her own. She tries but ends up screaming and crying.. so we try to calm her down, hush, sing and try not to pick up but it is not working. We do it over amd over in turns but no luck! She doesn’t stop unless we pick her up... and more importantly she gets really fussy and overtired and ends up not sleeping at all... After all, I end up putting her on breast and she falls a sleep and then I lay her back in crib while she is sleeping. If we are lucky she sleeps 2-3 hours...

Is there anyone out there who is successfully does it? I mean putting baby down awake but drowsy and make her sleep?