We played Sade on low and then we would lay along our forearm face down.. I'm sure you've tried that already. It still gets him to sleep on bad nights. even at 8 months old lol. Baths helped us too .

I lay my baby on his side, pull him close and rub his back. also a warm bath or warm washcloth over their tummy and swaddling

Hold him. He is probably in discomfort and the only real remedy to his upset moments is mommy. You cannot spoil a newborn. ❤ I think he probably just needs mama's warmth and heartbeat to settle himself.