Self soothing is a learned skill that literally takes weeks or months depending on your consistency. It's not something that will happen overnight, or within a few days.
As your LO matures, from 3 months to 4.5 months, their ability to settle into sleep gradually improves. It will take a lot of patience, lots of patting-shushing, and helping them through the jolts, but it will come with time…they are just learning!