Jackafina, new born babies do not have the capacity to self sooth. Babies can though learn to settle themselves, in time. 4 weeks is too young.
However I agree that you need to ensure you have changed and fed baby and checked there is nothing wrong. You are right to think this. But it will be several weeks before your baby is able to settle without you, and several more weeks before she will reliably settle most of the time without you.
Things you can do to encourage your baby to learn to self sooth. ..... Own cot, routine, constant room temperature, change baby before feeding and never the other way around, dark room, be quiet, little stimulation, swaddle them and tuck them in securely.
Mine both found their thumbs. DS1 (now 18) found his thumb before we even left the hospital! So we never had dummies, thumbs are always there! They can't throw them out of the cot or lose them. I gave both very small teddies they could grip in their hands. They were very attached to these. This helped.
Both slept through from about 11 weeks. And DS could be put down awake from about 6 weeks.
But you have to realise that if they are crying and can't settle they really do need you. So whilst you might try to create the conditions in which they settle on their own there will always be times when they can't.
Crying it out seems to work on the basis that a fractious grumpy tired baby exhausts itself to sleep. And it does, but at what cost to the child's mental well-being?