Even in the womb, a "baby" will self-soothe by sucking their fingers/thumbs. It's a natural instinct. I researched this, and many experts have said that it is good when a baby learns to self-soothe. Your girl very probably did this in your womb too, with her own fingers.
There is nothing "wrong" with self-soothing.. it is a natural instinct. Sure, in our culture it is frowned upon if a child gets "attached" to something to fall asleep. In other cultures, it is not. So, it depends, and on the Parent and their "stamina" to get their baby to sleep... peacefully.
Perhaps, try different pacifiers. Babies usually will take to the one they like... and reject others. Or, (with my son), he likes to cuddle his stuffed cow when he sleeps, and it helps him, and yes, my son uses a pacifier. It does not bother me or my Hubby. He can fall asleep by himself even though he is still awake when we put him in his crib.
There are many ways... each Parent uses different approaches. But bear in mind, that a "habit" will be formed with whatever "routine" you use to help a baby/child to fall asleep. And transitioning them to something else can take time.
For my firstborn.. she could only fall asleep if she was hanging on to my boob. She did NOT want anything else, although I tried in earnest. Now, she likes to have her dolly with her when she sleeps. So that's fine. Children/babies like to cuddle things. It's a phase and then sometimes not. Me, I sucked my thumb and had a blankie. My parents did not do that to me.. it was just something I gravitated toward. So, there are all kinds of different things.
Or perhaps, get your baby a "lovey" blankie... there are real cute ones from Amazon.com Just type in the search word "baby security blankets."
At your baby's age.. just be sure it is a "tiny" blankie so it does not get tangled up on her face etc., for safety.
Good luck, and take care,
~Susan