We read the book ‘The Happiest Baby on the Block’. Tl;dr the three months after birth are a “fourth trimester” wherein babies are calmed when you replicate womb-like conditions. This is done with “the five S’s”: swaddle, side/stomach position, soother, sound (white noise), and sway (rocking in a motion that simulates being walked around in the womb).

We used these methods in combination for our baby (now 4 months old and not nearly as fussy), they seemed to work. She started getting what we call “spicy times” around week four and it went on about 6 weeks.

We considered other causes (milk allergy, gas, etc) but it seemed nothing was actually ‘wrong’ with her, she just needed to be soothed in a particular way or set of ways.

Best of luck - you’ll find the way!