S., I waited to transition my co-sleeping baby until she was six months old because the general school of thought is that is the magic age when they're mature enough (neurologically and gastrointestinally) to sleep through the night without waking. At six mos., they don't need to feed throughout the night and it's not a convenience to have them sleeping right there to breastfeed anymore. I don't know if you're breastfeeding but it's something to consider. Also, because our baby's dad is such a noisy, restless sleeper, we had a white noise machine that played ocean/wave sounds which helped us all sleep better. Babies are used to a lot of noise in the womb and the sounds won't phase her at all, it may comfort her actually, and it will drown out your movements and/or any snoring or sleeping sounds, etc. In fact, we still use ours & if you like, you can look at Linens N' Things or Bed Bath Beyond, etc., for one. Don't worry too much about becoming dependent on the noise. I was a little concerned, but it hasn't proven to be a problem so far, since my baby goes to sleep plenty of other places without it.
Anyway, it may be a little early for your baby at four months (and crying it out isn't suggested until after they're six months old too, by the way), but you have nothing to lose by trying, so here goes. I read some great literature that encouraged setting up a bedtime ritual. Yours can be whatever you choose, but mine always went as follows at the same time every night and in the same order: playing & cuddling in early evening, dinner (yours may not be eating yet, so disregard), bath, nursing until drowsy in our bed and direct transition to her own bed from there. There was no playing or giggling like in the bath once we hit our bed. We'd come straight from the bath & dry off, put lotion on (the little massage helped her relax) and get into her sleep sack and swaddling, then nurse and wind down right away. I always put her to sleep swaddled - if I didn't, she didn't feel very secure and it wouldn't work. (https://www.halosleep.com/products/) And, the key was putting her in bed drowsy and not asleep, so that she knew she was in her bed, but too tired to care and then she didn't freak out when she woke up somewhere alone where she didn't actually remember falling asleep. It took about a week or so of this to get her in a good routine and if she did wake up and fuss as I was transitioning her to her own bed, she never fussed more than 10 minutes tops because she was already so tired and wound down from our bedtime ritual that she settled right in. Now, she's 15 months old and we still have the same exact routine, only we've added a book and a bottle of milk after her bath in our bed (instead of breastfeeding because she self-weaned at a year) before putting her to bed in her own room. Also, our baby's got night light and a musical mobile which she can also turn back on if she wakes up and she goes to sleep completely awake now with no crying and no trouble each & every night, I'm happy to say. We didn't have to swaddle her anymore too after about seven or so months. She went to a regular sleep sack and then regular jammies after that with no problems. The swaddling really, really, really helped ALOT!
Feel free to email me if you have questions. I remember feeling pretty anxious about putting Lily in her own room at first, but it went so well I couldn't believe it. We could just be lucky, but I really feel like it had to do with waiting until she was physically able to make the transition and then following through religiously and consistently with the bedtime ritual.
Sorry this is so long - I wanted to be really comprehensive & give you good suggestions. Also, I know everyone's got their own opinions, but my pediatrian gave me good, very well based reasons for not crying it out until AFTER six months of age by the way. They're still too young & dependent biologically until that point. Please check with yours before doing it. It's gut wrenching to hear your baby crying, but not as quite AS heartbreaking when you know physically they're needs are 100% met and they're just blowing off steam. Good luck!