Newborn infants usually sleep a lot (and wake a lot), and get tired very fast... so I guess, she is wanting the boob a lot?
Differentiate between her just being "tired" or her being hungry and needing to feed. And, infants usually fall asleep during/after nursing too many times. So it may just seem like she wants the boob when she's 'tired.' Infants can also "cluster feed"... meaning they nurse all the time, even every hour. But if they are not getting enough intake, then they are always hungry, thus wanting the boob, often....
Is she latching on properly and you can see her actually sucking and swallowing? Is the entire areola in her mouth? Is she nursing long enough to get to the hind milk? If she falls asleep or seems satisfied after nursing, then she is probably getting enough intake. But just feed her on demand, she's so young and they need it.
babies even 'suck' on their fingers in the womb... so, sucking is just an instinct and self-soothing. If it suits her, try the pacifier. My daughter didn't like it, my son did. It helped a great deal.
Either way, whether it is with a boob, a pacifier or a bottle... they will still have to 'wean' from it later... so pacifying takes all forms, human or not. It's okay. They won't go to college with it. LOL
Pacifiers comes in all sizes per the age of the baby. Just buy several kinds/brand and try it. That is, if you want to. Then perhaps just for sleeping, try and put it in her mouth.
Yes, if it falls out of their mouth, they can wake. Maybe or maybe not. Each baby is different. Once my son fell asleep, it would fall out. But he didn't scream or wake for it. As he got older, we just put about 3 paci's in the crib, and he could just grab one himself.
So many opinions on this subject.
At this age, can't really expect her to self-soothe... rocking/nursing etc., are comforts they need to sleep. They need Mommy and the bonding from us. Its just an instinct and for survival purposes. As she gets older... you can try and get regular about her nap/sleep times. But she's too young now.
My kids were both so different with sleep. My daughter was very high-demand, my son is not. So I just had to do what worked for each one & customizing it. And now, they are both great sleepers and nappers. I was more attachment oriented and co-slept as needed. So I'm one of those. Every Mom is different... cue into your baby and see what works. But at this age, we sorta have to keep up with their needs.
Well I don't really have a 100% solution, just some thoughts.
Good luck,
Susan