Letting baby “ cry it out “ ?

FTM here and just wondering seriously at what point do you let a baby cry it out . He’s only 3 weeks old but today I’ve literally done everything . Fed him , burped him , gas drops , clean diaper . Tried rocking him . Checked his clothes to make sure nothing was poking him and he still keeps crying . I finally got him to fall asleep but he keeps waking up in spurts of crying. I feel horrible letting him cry but I’ve literally done everything and am in tears myself 😭

Help!