Phase it out method for night paci weaning

LO is 4 months. Her pediatrician told us we cannot sleep train her yet and honestly I wasn’t really planning to until she got closer to 6 months anyways, but she encouraged us to begin helping her with healthy sleep habits. I feel like we already do this and have been doing this for a few weeks now. She has a solid daytime schedule, consistent bedtime routine, goes down for sleep awake with a paci, sleeps in her own room, etc. My end goal is to put her down without her paci eventually. She does alright with it currently. I do usually have to go in and replace it a few times until she finally falls asleep. After that, she really doesn’t mind if it falls out. But I don’t want it to ever become an issue of me playing the paci game with her at night, so I want her to be able to fall asleep without it, especially at night. What we have been doing the past few days to begin this process is my husband bounces her to sleep without the paci at nights and lays her down. I’m hoping this way we can slowly cut back on the time he bounces her and essentially phase him out until eventually he just stops all together. I am aware that once we commit to putting her down fully awake eventually, we will likely have some crying. But I hope it will be less than allowing her to continue falling asleep with the paci and then one night just cold turkey taking it. Has anyone tried this and had success or am I essentially going to get the same outcome regardless?