Newborn fussy

Hi mummies. My newborn is currently 1 mth+. She has a routine at night where will be fussy and it will usually start around the same timing eg 12 midnight til 3am. Gave her milk, change diapers, burp her, carry and hugged her. But she will still scream. And she will fall asleep at 3am cos by then thats when she will be tired from crying. Not sure what im doing wrong and i feel bad seeing my baby crying helplessly. Does any mummy experience the same? I hope im not alone Pls share tips for fussy baby if have any. Tq!